组卷网>知识点选题>单调性法求数列最值
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解答题 | 较难(0.4) | 2021·全国高三专题练习
1 . 各项不为0的数列eqId2c1230a9ef5a4968be599681d676dd2b满足eqId6e5a865ddebf4c3e8f88b1120f1f1d90,且eqId6b3bee9535ff4888ab6548f65616e44b
(1)求证:数列eqId50f78946aa7c473eaacde09afd7f8cbc为等差数列;
(2)若eqId1cbd10cfc6994f12883bb554b0ce7016对任意eqId075d44d1e421488b950d298144815f07恒成立,求实数eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c的取值范围.
更新:2021/07/31组卷:0
解答题 | 较易(0.85) | 2022·全国高三专题练习
2 . 已知首项为eqId6b2724baa0064c51b2ba39f5b281a1eb的等比数列eqId2c1230a9ef5a4968be599681d676dd2b的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqId318f638ef8bd45dc99aebe6e515bbee6,且eqId312da2db6b9c4f41841198fc58db17a5eqIdc76fa52010534e50926a7629658fd2b3eqIdace104ee1487497b85e88394d910f753成等差数列.
(1)求数列eqId2c1230a9ef5a4968be599681d676dd2b的通项公式;
(2)设eqIdd217812bfcb54fcabb79e170b44a8f36,求数列eqIdd478cd8b0b6040e1824cc4233b0f264a的最大项.
更新:2021/07/31组卷:0
3 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqId1b870f8b46dc466aa4eb8cceaae660c7eqId33eb691675fa4783a7d7b123d444c74f.数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade.
(1)证明:数列eqId0af7de3c1a70443392076802cca01819为等差数列;
(2)求eqIddb5481de79c946c0a760143297d5eade
(3)若不等式eqId06bb44aa40c14e129b9690c9e7bfabe5,对任意eqId9286163a63004a53a7334dc742be02d2恒成立,求eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c的取值范围.
单选题 | 较易(0.85) | 2021·四川射洪中学高一期中
4 . 若eqId43301ceb4fc24808a18fbce9a9492cb7为常数)eqId532dc4d959024b79b546428f5856e5aa,且数列eqId93e38ecd74a24cb59da79181b95bfd3a为单调递增数列,则实数eqId69f56ef2c88b4b73a560da59f5247a82的取值范围为(   )
A.eqIdd978a712c3e2490bb2fd95ff492a8e0fB.eqId4c98d34de0a74d0abb372271a934620dC.eqId06bdb06273c94e0f87f5537c8abf082dD.eqIdd24b2be0dc2a42049b2823fd091020c1
5 . 已知等比数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,且当eqId6c2146ec6df54fc9af9b2aef04489c8b时,eqIddb5481de79c946c0a760143297d5eadeeqId553ca58289c44e7ba04606445f2b5015eqIdcf4f7a91e7f54b3382c06e2bfa6fb85a的等差中项(eqIda4be99d332154d13a4a6ed1ff6444fe7为实数).
(1)求eqIda4be99d332154d13a4a6ed1ff6444fe7的值及数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式,
(2)令eqId5cc09118dc234b4ea8c440dafe6198a6,是否存在正整数eqId4d2187284c5d4de29906363f7d21f60f,使得eqIda3f30d87292a4a5285f9cbc53184c014对任意正整数eqId5f904d1376ac4de7a7d6cfea92ff6981均成立?若存在,求出eqId4d2187284c5d4de29906363f7d21f60f的最大值;若不存在,请说明理由.
解答题 | 较难(0.4) | 2021·上海师大附中高一期末
压轴
6 . 设数列eqId56ec9bffbd994c5fae7c3dce1b637ac7的前两项eqIdb7fe39c06a504b9a987ad9d3510bb8b1给定,若对于每个正整数n≥3,均存在正整数k(1≤kn-1),使得eqIdce85a3efcd6c44bf89b275ea33dc1a69,则称数列eqId93e38ecd74a24cb59da79181b95bfd3a为“eqIdc126eb5e474f44328981eb16a7eeb595数列”.
(1)若数列eqId56ec9bffbd994c5fae7c3dce1b637ac7eqIda7b1890b6e884edf8d2da13acb68a6e5的等比数列,当n≥3时,试问:eqIdef9cef8e6d054d8dac46b8cde14953adeqIdab781bc585fe400a98f50374b5ef8314是否相等,并说明数列eqId56ec9bffbd994c5fae7c3dce1b637ac7是否为“eqIdc126eb5e474f44328981eb16a7eeb595数列”;
(2)讨论首项为eqId75691f28a5bb4c8287401017aa3a2d29,公差为d的等差数列eqId93e38ecd74a24cb59da79181b95bfd3a是否为“eqIdc126eb5e474f44328981eb16a7eeb595数列”,并说明理由;
(3)已知数列eqId93e38ecd74a24cb59da79181b95bfd3a为“eqIdc126eb5e474f44328981eb16a7eeb595数列”,且eqIdfb732b17f71c4f1eb901c0b26012c46d,记eqId169b2b1e12f3443eaa15b9d6f6d71bc0,其中正整数kn-1,对于每个正整数n≥3,当正整数k分别取1,2,…,n-1时,eqIdbe48a92b29c24e4b957126cec4e597f7的最大值记为eqId1c7c01488de74ef0834b18ba2fb56e7d,最小值记为eqId3ace3c3d961c4c7b9e52b402b32aa5d5,设eqId30ba464505644cfe9c08ce632db7990d,当正整数n满足3≤n≤2021时,比较eqId45a6b09a4fd24aecb1eafc7cf40bb354eqIdf3cd588dd7a34486b87710d27feacb6c的大小,并求出eqId45a6b09a4fd24aecb1eafc7cf40bb354的最大值.
7 . 已知数列eqId83b64eb8a86246b9849cdebd89fc8f4f,且满足eqId541daa8685f84ffeaed84656909cdedceqId10a29cfa29b242d2bf11f16d29380d81eqId532dc4d959024b79b546428f5856e5aa
(1)证明新数列eqIdd0f23d3ccaf94a0cac3db2f560f94ab9是等差数列,并求出eqIdef9cef8e6d054d8dac46b8cde14953ad的通项公式.
(2)令eqIdb8d72f2ee23b4c91bb2b41513f58f849,设数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前n项和为eqIddb5481de79c946c0a760143297d5eade,求eqId122d8a3c9b4547dd9ef4805659a4929a的最大值,并说明理由.
解答题 | 一般(0.65) | 2021·浙江高三其他模拟
8 . 已知等比数列eqIde0b9732dccbd4cb1b604e897b552ab03.数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63满足eqIdd2b229fab4ad4b12b15251d3c3eda9cbeqIdd58667828ce74b2688d10ba5b960a6af
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3aeqIdeeb4ca98872f4e6d91cea28f43fc0b63的通项公式;
(2)设eqId785c2b02e8724e41b20d75e8a584877f,记数列eqId74ef5fe5183946caaee41d8974816a20的前n项和为eqIddb5481de79c946c0a760143297d5eade
①求eqIddb5481de79c946c0a760143297d5eade
②求正整数k使得对任意eqId494aaa42c6954e0d8dd1c58780cefa84,都有eqId8b7574820f1a474b9c00cbbd0fa90e27
填空题 | 一般(0.65) | 2021·陕西(文)
9 . 若数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqId190ab57c28aa4404b156e5927e534ec8,若eqId1245402095b94ff0a0c01f5d17660478恒成立,则eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c的最大值是______
10 . 高斯函数中用eqId7b5559fa52604169ac0cb99796b61142表示不超过eqIda9cd3f94eb8045438f75e9daccfa7200的最大整数,对应的eqId457faf5bce804854a5f3bfb0e803186aeqIda9cd3f94eb8045438f75e9daccfa7200的小数部分,已知数列eqIdef9cef8e6d054d8dac46b8cde14953ad的前eqId92478644b29a4a0e8470a8c89d31b49f项和为eqId58845b50fe34474e8d16601aa8ae5c1a,数列eqId88d3a678aa154f5ea70681dbfdeaeecc满足eqId74c3a40d700b462991aa50793b6e5fdb.已知函数eqIdd4097fb8cba74ce0b389d6764a7e69ebeqId01721b7f9e9c4f5ba8693e63794d4701上单调递减.
(1)若数列eqId1c4b7799989448aba8c59261414d9246,其前eqId92478644b29a4a0e8470a8c89d31b49f项为eqIddb5481de79c946c0a760143297d5eade,求eqIdbc24c6e646ef45d78124b2ff20ca875b
(2)若数列eqId0ceca5e49fa34c9fa417bc9d70a8a923(即eqId77a2e8ffb48c4c34aaf0642dcb68ac21eqId88d3a678aa154f5ea70681dbfdeaeecc的小数部分),求eqId77a2e8ffb48c4c34aaf0642dcb68ac21的最大值.
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