名校
1 . 若数列
,
满足
,则称
为数列
的“偏差数列”.
(1)若
为常数列,且为
的“偏差数列”,试判断
是否一定为等差数列,并说明理由;
(2)若无穷数列
是各项均为正整数的等比数列,且
,
为数列
的“偏差数列”,求
的值;
(3)设
,
为数列
的“偏差数列”,
,
且
若
对任意
恒成立,求实数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e901b990962dbb24d03f18c1aabc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea11bd18577ee314988bc70b0caf23f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639e35fe876a1b682123bbc739ffccda.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc361145f10976ad26726a25902af91e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4a2ab6d0957e52a1242e6d899be539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d1512b9a0d9d79f8b71ced14eacd85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee632cfe1cc460fbcd32b9e8a630a543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2019-12-02更新
|
669次组卷
|
9卷引用:上海市行知中学2020-2021学年高二上学期10月月考数学试题
2 . 从数列
中取出部分项组成的数列称为数列
的“子数列”.
(1)若等差数列
的公差
,其子数列
恰为等比数列,其中
,
,
,求
;
(2)若
,
,判断数列
是否为
的“子数列”,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec07a126ada2c921c5b4337f77854cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaa992a449b828df0ff545e233b279b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84f592310f4b9637b225cab622b2aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d438131add92b51c4e0b06ec6aff581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373ecb5531c1593f13a0ed081597b3cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9d38a1171131b1a1f3f70ca2117be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221016d4bfafd5693a4e767fcf6a2559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2019-11-14更新
|
370次组卷
|
3卷引用:上海市闵行区七宝中学2018-2019学年高二下学期开学考试数学试题
上海市闵行区七宝中学2018-2019学年高二下学期开学考试数学试题上海市七宝中学2018-2019学年高二下学期3月月考数学试题(已下线)4.2 等比数列的前n项和(第2课时)(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件(沪教版2020选择性必修第一册)
3 . 对于数列
,若存在正数p,使得
对任意
都成立,则称数列
为“拟等比数列”.
已知
,
且
,若数列
和
满足:
,
且
,
.
若
,求
的取值范围;
求证:数列
是“拟等比数列”;
已知等差数列
的首项为
,公差为d,前n项和为
,若
,
,
,且
是“拟等比数列”,求p的取值范围
请用
,d表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2348d5068480809ea002ebc2d3261b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355ecdd4f11a834b239d3372fdad79cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f515802d3e4a059101262543d9539f89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2348d5068480809ea002ebc2d3261b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c13a7c5f125946dc9e66f415274bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f059e451fc147d98681d846e5dff60c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4786298021b32d1157d8cfed1dd32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2348d5068480809ea002ebc2d3261b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ad1fb1d7620bbe82f7b2fc898884a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6431e38fd3c017039a3165a88fd1bd4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec2b1d696c335742118ddc277c3aa31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5da156caade01a5d043c4f1c4cf2a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9088ca88713b67fe8f9800b4c0098b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33234b1dfb648c2841a95ce41a811338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f38b66be80efa410b2af2ddb98c199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48281ebfef252e3ce321372e3c5f8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ce0f2dcc52de2178221411580e2becb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0998d4efc4bec196abda648f2843b2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81c68c6e1ecc9657768b37ce4ac1767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550b38661c751d2cd439441288c53959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae7c412ecf39813bdd9aaa368519954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee5202ea0177811a3bbda746c13ea4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ce0f2dcc52de2178221411580e2becb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0998d4efc4bec196abda648f2843b2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
您最近一年使用:0次
2019-03-18更新
|
600次组卷
|
3卷引用:上海市行知中学2020-2021学年高二上学期10月月考数学试题
4 . 如果数列
,
,
,
(
,且
),满足:①
,
;②
,那么称数列
为“
”数列.
(1)已知数列
,
,
,
;数列
,
,
,
,
.试判断数列
,
是否为“
”数列.
(2)是否存在一个等差数列是“
”数列?请证明你的结论.
(3)如果数列
是“
”数列,求证:数列
中必定存在若干项之和为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140b9dbcada4ac2e5fe3cc30009bcd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/573394d925f221e828978ba5b528dd39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/527093b2ec760913d0dccff8a099248b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc27b9585a488e814695f51c47a2f32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc6d901b61ca0b350e3751486fbc9d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d590075ddd8450d14197ac5948df9de6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c6c10b18ec2e35aae7caa645c44665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab8d6252ef31c00ac52ca20605610367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
(2)是否存在一个等差数列是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
(3)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
您最近一年使用:0次
5 . 如果数列
满足“对任意正整数
,都存在正整数k,使得
”,则称数列
具有“性质P”.已知数列
是无穷项的等差数列,公差为d
(1)若
,公差
,判断数列
是否具有“性质P”,并说明理由;
(2)若数列
具有“性质P”,求证;
且
;
(3)若数列
具有“性质P”,且存在正整数k,使得
,这样的数列共有多少个?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320e7710ac9aafc0ecaf91ba6686cea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab406d94b4907ab8a20ae3214628b045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f2572192cc7ca046e9a3155ef3e56a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3068733ef2ceda9f1620d5c9bcdfa542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8e68eb4ade6e22982d2df5102d8894.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0af74258551ca3f28b2c6ce54bffd1.png)
您最近一年使用:0次
2018-05-04更新
|
720次组卷
|
5卷引用:北京市第五十七中学2021-2022学年高二下学期期中考试数学试题
6 . 对于每项均是正整数的数列
,定义变换
将数列A变换成数列
.对于每项均是非负整数的数列
,定义变换
将数列B各项从大到小排列,然后去掉所有为零的项,得到数列
.又定义
.设
是每项均为正整数的有穷数列,令
.
(1)如果数列
为2,6,4,8,写出数列
;
(2)对于每项均是正整数的有穷数列A,证明:
;
(3)证明:对于任意给定的每项均为正整数的有穷数列A0,存在正整数K,当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16b0ed0e5badee7d373e748ec171249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba4c7f82d79d6efcfdf7177471874b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7ccb439f9a7212c90ab2e2abe2aa66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01cb697da92064ad1d9144e4f12be365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94cb0d60922f9e9e5a37b3085b59e7b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f610650fae8e1f446b736e608061a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2569b63ebc4bd9b2334f4ef3f1fa1565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b9d53a1b78bcd6222e3899d330a149.png)
(1)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2988e435ffb7935d49569ee824262f.png)
(2)对于每项均是正整数的有穷数列A,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4a4656523b5985571edfdd09340639.png)
(3)证明:对于任意给定的每项均为正整数的有穷数列A0,存在正整数K,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b6ba2966874d33da6b94662d7cb23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d11b12b9af98c4b0bd2a150abeb6227.png)
您最近一年使用:0次
7 . 设数列
满足:①
;②所有项
;③
.设集合
,将集合
中的元素的最大值记为
,即
是数列
中满足不等式
的所有项的项数的最大值.我们称数列
为数列
的伴随数列.
例如,数列1,3,5的伴随数列为1,1,2,2,3.
(1)若数列
的伴随数列为1,1,2,2,2,3,3,3,3,请写出数列
;
(2)设
,求数列
的伴随数列
的前50项之和;
(3)若数列
的前n项和
(其中
为常数),求数列
的伴随数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b270a87d8e670809520e33c85bc3899a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd992f0b72c282959031890e58c7810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ccd7443fe60322b99e116a523a33207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64696f60c533ad95dc7890eb902741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64696f60c533ad95dc7890eb902741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19db2869aeaf97debfa2e2f9a4843a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
例如,数列1,3,5的伴随数列为1,1,2,2,3.
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb1ca762c8207aaa6fcb6406d224f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac84359e567db7ab2e55b1de8342622a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e74be91bfe4bc209da7539dbf9b72c.png)
您最近一年使用:0次
2018-04-03更新
|
764次组卷
|
3卷引用:北京市良乡附中2022-2023学年高二6月月考数学试题
8 . 已知数列1,1,2,1,2,4,1,2,4,8,1,2,4,8,16,
,其中第一项是20,接下来的两项是20,21,再接下来的三项是20,21,22,依此类推. 设该数列的前
项和为
,
规定:若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188596a6765896c794118d3a39dc0fab.png)
,使得
(![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e84b6d7d85ca0f0bb173f209a909c7c.png)
),则称
为该数列的“佳幂数”.
(1)将该数列的“佳幂数”从小到大排列,直接写出前3个“佳幂数”;
(2)试判断50是否为“佳幂数”,并说明理由;
(3)(i)求满足
>70的最小的“佳幂数”
;
(ii)证明:该数列的“佳幂数”有无数个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
规定:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188596a6765896c794118d3a39dc0fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858911660b233271d57b17e358232d45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d76a1197aaabd0077aafc8d6e850747d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e84b6d7d85ca0f0bb173f209a909c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad135b14c9dcd83eab6618d7694c7b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)将该数列的“佳幂数”从小到大排列,直接写出前3个“佳幂数”;
(2)试判断50是否为“佳幂数”,并说明理由;
(3)(i)求满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(ii)证明:该数列的“佳幂数”有无数个.
您最近一年使用:0次
2018-01-26更新
|
663次组卷
|
3卷引用:江西省抚州市崇仁一中、广昌一中、南丰一中、金溪一中四校2023-2024学年高二下学期第二次月考数学试卷
江西省抚州市崇仁一中、广昌一中、南丰一中、金溪一中四校2023-2024学年高二下学期第二次月考数学试卷北京市昌平区2018届高三上学期期末考试数学(理)试题(已下线)微考点8-1 新高考新题型19题新定义题型精选
名校
解题方法
9 . 若有穷数列
(
是正整数),满足
即
(
是正整数,且
),就称该数列为“对称数列”.例如,数列
与数列
都是“对称数列”.
(1)已知数列
是项数为9的对称数列,且
,
,
,
,
成等差数列,
,
,试求
,
,
,
,并求前9项和
.
(2)若
是项数为
的对称数列,且
构成首项为31,公差为
的等差数列,数列
前
项和为
,则当
为何值时,
取到最大值?最大值为多少?
(3)设
是
项的“对称数列”,其中
是首项为1,公比为2的等比数列.求
前
项的和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecb97979f93c90fcf4baa7b7106abb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7953bb514daa500885e892857678f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22fc26a14e8e5987688565881fb71e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b266d811e20740699ab629767b43e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1122d70cf267893185983de9d811729.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f6714682274c31a328bf796e235900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc5a47eb206ee12c7f65ea26fc26e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64fcc69dc28bc11b22f5c9bec9e2aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ada2c9f82459340da96274ee60ffbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cba4fcd5b19e52391aa57127aa39b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0fcf02ab751cc3910a0bc0872ac2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05201ef79a5d5904f492845396fb5470.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8746bc092f553f33ce1a0d8d2b7b28d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be881773917095d173260995ffacfd0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897d8f6cf00391f1b3ff70432f0121b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31ec8dee46f3affe69cbdb2abbe8feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31ec8dee46f3affe69cbdb2abbe8feb.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50d1705a68b70921f86dd10020420b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24de9307bdb075bfc55d86d35e54ed57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50d1705a68b70921f86dd10020420b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f1dd3b69d0e8157998cc59efedb022.png)
您最近一年使用:0次
2017-07-02更新
|
219次组卷
|
2卷引用:湖南省长沙市明德中学2016-2017学年高二上学期阶段测试数学试题
10 . 数列
对于确定的正整数
,若存在正整数
使得
成立,则称数列
为“
阶可分拆数列”.
(1)设
是首项为2,公差为2的等差数列,证明
为“3阶可分拆数列”;
(2)设数列
的前
项和为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cddbe3254149affeb78f1a8e480cda2e.png)
,若数列
为“
阶可分拆数列”,求实数
的值;
(3)设
,试探求是否存在
使得若数列
为“
阶可分拆数列”.若存在,请求出所有
,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f1989d2fdc0158e468791c4a8238138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cddbe3254149affeb78f1a8e480cda2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d70091a41063af1169dbc1762e9583e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5820011dec0ecc428c4926efd82d9b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2017-06-29更新
|
844次组卷
|
2卷引用:上海交通大学附属中学2023-2024学年高二上学期10月月考数学试题