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首页>高中数学综合库>数列>数列的概念与简单表示法>递增数列与递减数列>判断数列的增减性
题型:解答题 难度:0.15 引用次数:167 更新时间:2020/5/20 10:29:52 题号:9868531
已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqIdf458db68122849abb588feb2e682d9ac项和为eqIddb5481de79c946c0a760143297d5eade,且满足eqId35c5b2bf33b64f0a8cbeedc42717d803eqIdbce7c9fbfb41451cb656361fd7b48ad6,设eqId89b299df551f4e46b49413ed77fc65e2eqIdc73ad4de0ec14cba91db08ec61124907.
(Ⅰ)求证:数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63是等比数列;
(Ⅱ)若eqId89504540b7c44fc49d836798d0382095eqIdc73ad4de0ec14cba91db08ec61124907,求实数eqId70a27b6ddf6b478285353abb3b1f3741的最小值;
(Ⅲ)当eqId06cc9b4949ce4809a05ce82e20fa6282时,给出一个新数列eqIda5fe2f95aaf64969913b1e71a2160965,其中eqId4ed5523a2e7d4c11bd1361d2a0fad8f6,设这个新数列的前eqIdf458db68122849abb588feb2e682d9ac项和为eqIdcd8b006a766b441896481934ce8624da,若eqIdcd8b006a766b441896481934ce8624da可以写成eqIddfa8c407d51f4755b02a7efe4960c1e4eqId32454977564e4ee18da36bd51156c509eqId34183d6823814508bb3a469860ca3c01eqIdd1676c2740214139bd95cdd3d448c3d0eqId3ae5584e22d94db98f02990ea85c2c0d)的形式,则称eqIdcd8b006a766b441896481934ce8624da为“指数型和”.问eqId558c17324d4f40c8b990a5f077e40f0c中的项是否存在“指数型和”,若存在,求出所有“指数型和”;若不存在,请说明理由.

类题推荐

【推荐1】设数列eqId315af7e63b0e4f1d93184bcb531e1e5aeqId2948528024544723855a13245532bc60满足eqId3d4b6dd5c5cd4041a0404ef7d7d3fa8e
(1)若eqIdba19a30e8edf40b88df53cbebee355f7,数列eqIdfc8f97c338064f19b3742698d0ed2dc5的前eqIdf458db68122849abb588feb2e682d9ac项和eqId7eba5c415e4445f29793da0436c3dae7,求数列eqId2948528024544723855a13245532bc60的通项公式;
(2)若eqIdfb3120ec10224237809363a0e1d11180,且eqIded61289d2244436faed5819e375abd1a
①试用eqIdded20d482be4465298882eae04d1cc07eqIdf458db68122849abb588feb2e682d9ac表示eqIdd63dfac5d90049639b81acb76fe20cc4
②若eqIdf460d777e9d04514b1b941c1ee256e76,对任意的eqIdde033a5da29942aaba3d65d308a68f73试用eqIdded20d482be4465298882eae04d1cc07表示eqId605d2d7cb933449487ef8952d3f78e9f的最大值.
更新:2018/07/06难度:0.15题型:解答题组卷:429
【推荐2】已知正项数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqId681ee32b0980433e94ff5b7e029a5760,且eqId305209c24b5347bf83edada4546a2497,设eqId6bd1cbdfdea34607a02c0484e2c7286b
(1)求证:eqIde8e9f7adfac8452bb3cb26b3ca4538b3
(2)求证:eqIdb80e617bfcdb4845b60fe393f7687a61
(3)设eqIddb5481de79c946c0a760143297d5eade为数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqIdf458db68122849abb588feb2e682d9ac项和,求证:eqId034dc89bb8544c27a36df0873ca3a8c7.
更新:2019/10/18难度:0.15题型:解答题组卷:184
【推荐3】已知项数为eqId8bb4fc61cb614f808bd59707326bb658的数列eqId2c1230a9ef5a4968be599681d676dd2b满足如下条件:①eqId5ba8a9c091c84dea9466c41ee515a017;②eqIdc81270e86f3a4b2b8f4c09caa181e8aa.若数列eqIda0db2906046940e19de8782f94f34137满足eqId66378f83c7e147d4b74c87f0adf6784d,其中eqId0cca985a0b124d778757751090c0d063,则称eqIda0db2906046940e19de8782f94f34137eqId2c1230a9ef5a4968be599681d676dd2b的“伴随数列”.
(1)数列1,3,5,7,9是否存在“伴随数列”,若存在,写出其“伴随数列”;若不存在,请说明理由;
(2)若eqIda0db2906046940e19de8782f94f34137eqId2c1230a9ef5a4968be599681d676dd2b的“伴随数列”,证明:eqId3ce0944835544504b555bcd2805ab64b
(3)已知数列eqId2c1230a9ef5a4968be599681d676dd2b存在“伴随数列”eqIda0db2906046940e19de8782f94f34137,且eqId77b3f6b9955e499dbdab033a38779496,eqIde47e51479a41424c9faeaaac708961f1,求m的最大值.
更新:2020/02/11难度:0.15题型:解答题组卷:167