1 . 定义:对于数列
,若从第2项起,每一项与它的前一项之差都大于或等于同一个常数
,且小于或等于另一个常数
,则
叫作类等差数列(若
,则
是等差数列).
(1)若类等差数列
满足
,
,
,
均为已知数,请类比等差数列的通项公式,求出数列
的通项不等式(即第
项
与首项
及
的不等式关系,要求写出推导过程);
(2)若数列
中,
,
.判断数列
是否为类等差数列,若是,请证明;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d48141571f43bdb1211a62edf02a011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(1)若类等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c57b3ca3af4f43d8ea2699f05cc8014e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecf9a2cfa6d5cba8c0b6c61dbf1235c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf2f1c1409a06278e847e6b573cef254.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddda8e6c1ea80647c96a6b89ee544e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
您最近一年使用:0次
2 . 已知数列
与
满足
(
为非零常数),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)若
是等差数列,求证:数列
也是等差数列;
(2)若
,
,
,求数列
的前2025项和;
(3)设
,
,
,
,求数列
的最大项和最小项.
![](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/998926638c7b8a50714455fb2c81693b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfec4233214c3a729c843dee0d186db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc578e720c84a0eedc00b06b08f14d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaf2a2590bb84d646957f913d78f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b9d521d0db9cf460c885225c2aa61f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0553383350144196c1122a26a188e343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
3 . 对于正整数m,n,存在唯一的自然数a,b,使得
,其中
,我们记
.对任意正整数
,定义
的生成数列为
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874689ac8a6f70ecd93aa1aaf7d626f6.png)
.
(1)求
和
.
(2)求
的前3项.
(3)存在
,使得
,且对任意
成立.考虑
的值:当
时,定义数列
的变换数列
的通项公式为
当
时,定义数列
的变换数列
的通项公式为
若数列
和数列
相同,则定义函数
,其中函数
的定义域为正整数集.
(ⅰ)求证:函数
是增函数.
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad12b60594a6408ccc237cad2880088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff38a5b95f1fb452d87fce9c80b1249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574aa06d3d4f9952157c60ec8f40b839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5914cd027a87542e12cfb0c92c0aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874689ac8a6f70ecd93aa1aaf7d626f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dbb663375b927f3c00d1be3fda1508.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37dbd8745cf6246eea337a1bf91258c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87dc8de41005802093ae66c08f46a7a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926145a2b2232a88ceed6e69dc050265.png)
(3)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623ebc0f0eba98e8f63b7cd982c11009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8144524289a76dadf88c02976acea2db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf0ce448d146abfcd0bd689b925d168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c20d94765a05ee86edf370dd64fcff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5914cd027a87542e12cfb0c92c0aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d054e320d843bf0ca4a620519f75ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8121a889da1f3ecbecd5387a9473c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98b98330b62847c220ab2f127e11391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5914cd027a87542e12cfb0c92c0aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d054e320d843bf0ca4a620519f75ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf19212dd24556423636ce37034cdf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d054e320d843bf0ca4a620519f75ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96dbc1106da9238ec6300e13ca3d9b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46498efb2e485c1172abe2189e498613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88ba8e1dc91318d8a9e1856d8ae080e.png)
(ⅰ)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88ba8e1dc91318d8a9e1856d8ae080e.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee5e2ada7f1e99bf68508d21b8f6fb7.png)
您最近一年使用:0次
4 . 设
.在
的方格表的每个小方格中填入区间
中的一个实数.设第
行的总和为
,第
列的总和为
,
.求
的最大值(答案用含
的式子表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f98da45d4de19a962cfa1d186e2755a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ace7d64e7ff100db25a07330654d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af908bca1b10f5de7e2d8979989c806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aba126d3f244b529547fa33b1dc5f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a71c7129333f890292aa75bc1d080a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
5 . 悬链线是平面曲线,是柔性链条或缆索两端固定在两根支柱顶部,中间自然下垂所形成的外形.在工程中有广泛的应用,例如悬索桥、架空电缆都用到了悬链线的原理,经过很长时间的探究,在17世纪末期,莱布尼兹和伯努利利用微积分推导出悬链线的方程是
,其中c为曲线顶点到横轴的距离.当
时,称
为双曲线余弦函数.
(1)解方程
;
(2)双曲余弦函数的导数成为双曲正弦函数,记作
.当
时,求
的最小值;
(3)已知
,求数列
的最大项.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ca69db0b421339c0658b8a5ddfdfb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed02acb0c7b4e40c26f6760627a033e.png)
(1)解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c1d8faec71e5860fd8fe0380edef8b.png)
(2)双曲余弦函数的导数成为双曲正弦函数,记作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c540f798ab69463cf35af2772a3a19cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d25e73fea1d7f3ddfe86e3f270aaac.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7613e08bfdad2a3cf0e837b5f1ad6adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cd85fbaf162fc0b3060080b2b5ff459.png)
您最近一年使用:0次
名校
6 . 已知数列
的通项公式是
,数列
是等差数列,令集合
,
,将集合
中的元素按从小到大的顺序排列构成的数列记为
.
(1)若
,写出一个符合条件的
的通项公式,并说明理由;
(2)若
,且数列
在
上严格单调递增,求实数
的取值范围;
(3)若
,数列
的前5项成等比数列,且
,试求出所有满足条件的数列
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12059d1dac926a235ccd40c3b61b1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a2cc9d707670230d444e9f21c53648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b132c9d395856f385713dd6c90cad80f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153c6891b653364fbea00d9793f961a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b8bc5cd0869697abac312c4cf0525b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2771c5f04582c545e0f9afc8a2cb9597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2853db0b85e810be7d37f2643c132a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
名校
解题方法
7 . 已知数列
满足
,
;
(1)设
,
,
,求证:数列
为等差数列,并求出数列
的通项公式;
(2)设
,
,
,数列
是否有最大项,最小项?若有,分别指出第几项最大,最小;若没有,试说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbdfea553673d342e6e2af7e249594b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86657d38b9096c971b3992c10446dece.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31607b5b01fcba994a4baefb97dc15d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22761709d37f9a2efaa8456e2dbdb054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
您最近一年使用:0次
名校
解题方法
8 . 1.设数列
中前两项
、
给定,若对于每个正整数
,均存在正整数
使得
,则称数列
为“
数列”.
(1)若数列
为
、
的等比数列,当
时,试问
与
是否相等,并说明数列
是否为“
数列”﹔
(2)讨论首项为
、公差为
的等差数列
是否为“
数列”,并说明理由;
(3)已知数列
为“
数列”,且
,
,记
,其中正整数
,对于每个正整数
,当正整数
分别取1、2、…、
时,
的最大值记为
,最小值记为
,设
,当正整数
满足
时,比较
与
的大小,并求出
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a22f5023293a85d8381277769d68dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53c09fba64f3bc86dac3e29bf56b018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b608c12c4e7b9e6d7561be763c6733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a22f5023293a85d8381277769d68dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9dae8e6c9b93458f324f30538a3eb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0055ef3b9c21a572f6cc0a79cdce9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a22f5023293a85d8381277769d68dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)讨论首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f966272f7781790ff27e40db6b525253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07186f6469ba083a12864ddee551246.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918893290e48bba154bd5a14a805f10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aadf9ab510510120699c5eee39ab18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf57ba4761db4d3fc993ae5815325bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a625b91e0eba33b107550ee2a1e2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717d039b3a4967ca6b0a899bfd12a83b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268b0a589ddfd494ebc898a556c260bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95931effbd59c43e8ed1ea09962b84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
您最近一年使用:0次
2021-12-10更新
|
812次组卷
|
4卷引用:江西省安福中学2021-2022学年高二上学期开学考试数学(理)试题
江西省安福中学2021-2022学年高二上学期开学考试数学(理)试题(已下线)专题03 《数列》中的压轴题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)上海市上海师范大学附属中学2020-2021学年高一下学期期末数学试题上海市格致中学2022届高三上学期12月月考数学试题
9 . 对于无穷数列
、
,
,若
,
,则称数列
是数列
的“收缩数列”,其中
、
分别表示
中的最大项和最小项.已知数列
的前
项和为
,数列
是数列
的“收缩数列”.
(Ⅰ)写出数列
的“收缩数列”;
(Ⅱ)证明:数列
的“收缩数列”仍是
;
(Ⅲ)若
,求所有满足该条件的数列
.
![](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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4b279f31a9ebd5d03ee171e7134a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e36bff57bcfa86432b340e25e51d42.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/f8424af9108fc00fbf86a3d5c9409e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689a822a0d8b276fbe8596a2f94f7022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41dd42e4f493477fb0f36137893d4d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅰ)写出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47dee512e0fdb19fc03858ce717ce8b7.png)
(Ⅱ)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(Ⅲ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66c1201efe37bb0f8db97f93459d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2021-05-29更新
|
809次组卷
|
2卷引用:北京市首都师范大学附属中学2021-2022学年高二下学期期中考试数学试题
10 . 已知无穷数列{an},对于m∈N*,若{an}同时满足以下三个条件,则称数列{an}具有性质P(m).
条件①:an>0(n=1,2,…);
条件②:存在常数T>0,使得an≤T(n=1,2,…);
条件③:an+an+1=man+2(n=1,2,…).
(1)若an=5+4![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
(n=1,2,…),且数列{an}具有性质P(m),直接写出m的值和一个T的值;
(2)是否存在具有性质P(1)的数列{an}?若存在,求数列{an}的通项公式;若不存在,说明理由;
(3)设数列{an}具有性质P(m),且各项均为正整数,求数列{an}的通项公式.
条件①:an>0(n=1,2,…);
条件②:存在常数T>0,使得an≤T(n=1,2,…);
条件③:an+an+1=man+2(n=1,2,…).
(1)若an=5+4
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cba79639deae5f8af6088b30c1a800.png)
(2)是否存在具有性质P(1)的数列{an}?若存在,求数列{an}的通项公式;若不存在,说明理由;
(3)设数列{an}具有性质P(m),且各项均为正整数,求数列{an}的通项公式.
您最近一年使用:0次
2021-05-02更新
|
1166次组卷
|
5卷引用:河南省洛阳市第一高级中学2022-2023学年高二下学期3月月考数学试题