名校
解题方法
1 . 高斯是德国著名的数学家,享有“数学王子”的称号,人们把函数
,
称为高斯函数(其中
表示不超过x的最大整数,例如:
,
).已知数列
的首项
,前n项和记为
.若k为函数
,
值域内的任意元素,且当整数
时,都有
成立,则
的通项公式为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e3204e4dc47a448860779349efcedf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87ea02e718c638f94174db08de61ea3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef1aed47b3da7febc5379a7d46773c9a.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab988b91d5de8edf58c54db012c2e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52eecd38954cd0ca3fb26328a39bb859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf70a562d0cdfa53595c7893d706e46c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2 . 已知函数
,数列
是公差为2的等差数列,若
,则数列
的前n项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ce49f7feb5cdf835afab65b2429cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99381f1c98c1d68d2768b805f181e54b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
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3 . 已知函数
,令
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6984d11b79b3b4222178dec44c0e4288.png)
,若
,
表示不超过实数
的最大整数,记数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f84517382ee52f6ac971d69150a4f2.png)
_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3dfa120b93866dca3dd706bbb8e178f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fc51ae6ba348d0e4d3765a4818406e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6984d11b79b3b4222178dec44c0e4288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5bc2b05dc79b18ecb4ac3f9b5c492d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a915ae795e3d6a8539a6e505ebf63685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23145dde872b37ef225d66504b43e21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26f05e2c86a700a657f06531e2f2458.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/d6f84517382ee52f6ac971d69150a4f2.png)
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4 . 已知8个非零实数a1,a2,a3,a4,a5,a6,a7,a8,向量
,
,
,
,给出下列命题:
①若a1,a2,…,a8为等差数列,则存在
,使
+
+
+
与向量
共线;
②若a1,a2,…,a8为公差不为0的等差数列,向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c47e4009bc0519a5f410bcf346b225a.png)
,
,
,则集合M的元素有12个;
③若a1,a2,…,a8为等比数列,则对任意
,都有
∥
;
④若a1,a2,…,a8为等比数列,则存在
,使
·
<0;
⑤若m=
·![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1211a8569149cb7439436d6600e42d06.png)
,则m的值中至少有一个不小于0.
其中所有真命题的序号是________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fbca1b06246b6b45587fe1dadfe9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b5c5c2bc9019843fcec02a56dd449d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/173d79326fcd634bdb761e073d00dc3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8898a138da96add88de8e42930510e3.png)
①若a1,a2,…,a8为等差数列,则存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d7cab8b0eb1e13d6972815822562f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0241b75bbf58e96ad5e016972b011027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196de9f558dc50d6cbf537e390d74427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab5cabb08427276c7b66c5e1f15a043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fda22bc688d523c3f333f8f08e0806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c47e4009bc0519a5f410bcf346b225a.png)
②若a1,a2,…,a8为公差不为0的等差数列,向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c47e4009bc0519a5f410bcf346b225a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e17d85712113ccc3be3b6cf9322e2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e1795935bb1b2d95ebda02ce245531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e2cd38ee3d1bb54155d6b526f9a10e.png)
③若a1,a2,…,a8为等比数列,则对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a60f82e6dd06b8d9228cbfcce5ab0d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/124c9843b7570e01a8e6d4951b508103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1211a8569149cb7439436d6600e42d06.png)
④若a1,a2,…,a8为等比数列,则存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a60f82e6dd06b8d9228cbfcce5ab0d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/124c9843b7570e01a8e6d4951b508103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1211a8569149cb7439436d6600e42d06.png)
⑤若m=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/124c9843b7570e01a8e6d4951b508103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1211a8569149cb7439436d6600e42d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355edb1bf5a0ccce114aa9e3afdf2c53.png)
其中所有真命题的序号是
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2016-12-03更新
|
1631次组卷
|
2卷引用:2015届四川省资阳市高三第三次模拟考试理科数学试卷
2011·四川绵阳·一模
5 . 下列命题中,正确的是_________ .(写出所有正确命题的序号)
①在直角三角形中,三条边的长成等差数列的充要条件是它们的比为
;
②设
是等比数列
的前
项和,则公比
是数列
、
、
成等差数列的充分不必要条件;
③若数列
满足
,
,则
;
④在数列
中,若
、
都是正整数,且
,
,
,
,
,则称
为“绝对差数列”.若一个数列为“绝对差数列”,则此数列必含有为零的项.
①在直角三角形中,三条边的长成等差数列的充要条件是它们的比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d44d5798d856568f7f6e5e91269ad5.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/2c68209e67ef5fe2ea3ce128f17c9799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05201ef79a5d5904f492845396fb5470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48e81b54f78b96294295542b010dfb.png)
③若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/945afd3b95878aeb361eef24a5a2e1ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069d9d8078168940cd9c246bd88531cb.png)
④在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/ba2e73c8f5511cab6dc67399f50afb29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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