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解答题 | 较难(0.4) | 2021·北京高三二模
1 . 设数集S满足:①任意eqId59864bbe61664c7b8503b12ebc3ba14e,有eqIdd7caa801b59d4def90d2fdb94a9b1c7c;②任意eqIdb9afacbb79e04cb3b35aef7f3d8b522c,有eqId2ee2c37abbd440d9bb5ab30bc4433fa6eqIdf20c6cfe343a483db1192ba799c5ecac,则称数集S具有性质P.
(1)判断数集eqIdc00799876a054f98b1c6b47aed1c1578是否具有性质P,并说明理由;
(2)若数集eqIdc9851c3c92504d62972181e7b3e3a817eqId9c2f742584ba4549b893c6f73a186765具有性质P.
(i)当eqIdd9440b6bbe65460ba49ccdd0583b5118时,求证:eqIda718e4d4d2164a8490c93e9ae3dc7a4e是等差数列;
(ii)当eqIda718e4d4d2164a8490c93e9ae3dc7a4e不是等差数列时,写出n的最大值.(结论不需要证明)
多选题 | 一般(0.65) |
同步
2 . (多选题)数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqId6f59d4ef96d74b37b47b3709b40e507feqId6bcd8228e445447cad3618f77490852e,则以下说法正确的为(   )
A.eqId61a767536ac34bbe9d04ef411975ffb1
B.eqId3e8ab08dde9945618672ab02c7697d73
C.对任意正数eqIdaea992e70d4943e49e893817eb885ed7,都存在正整数eqIda4be99d332154d13a4a6ed1ff6444fe7使得eqId76758f90ad444c0c886e13d8f8170aae成立
D.eqId9a9740c83433426784c72976d1f03f66
更新:2021/03/12组卷:205
解答题 | 一般(0.65) | 2019·四川眉山市·高一期末
3 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a为递增的等差数列,eqId3fbaa1ce275d4d8c9dfcd5b2ece6a936eqIdaf0b75b1017e44488651ddf9e14c20afeqId99efef6ee7e6459bbb489fafbc1b0cef,其中eqIdecb85257b56b444b9be309223313b187
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)设eqId76032e99f52b40ae95630cf28618acca,求数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqIdf458db68122849abb588feb2e682d9ac项和eqId92ed363a54bd4a8a93df9463bb3af1f5
(3)设eqId43d3a66909bf4e67b27ac41d129ef056,求使不等式eqId0658d0ffaa8a4c65997c56804fe66bcf对一切eqId6c2146ec6df54fc9af9b2aef04489c8b均成立的最大实数eqId0c243e5dded24989821daf9bef2676a6
解答题 | 一般(0.65) | 2019·上海市南洋模范中学高二月考
4 . 设正数数列eqId054d5a7de5684002909fe944c86227c2的前eqIdf458db68122849abb588feb2e682d9ac项和为eqIddb5481de79c946c0a760143297d5eade,对于任意eqId532dc4d959024b79b546428f5856e5aaeqIddb5481de79c946c0a760143297d5eadeeqId6be932a5bf5f4bb8bef8452d83d1842beqIdef9cef8e6d054d8dac46b8cde14953ad的等差中项.
(1)求数列eqId054d5a7de5684002909fe944c86227c2的通项公式;
(2)设eqId238052e290694517a852e70fd8559c2deqId92ed363a54bd4a8a93df9463bb3af1f5eqId69fa66742e6b480eb0e55f574b8b7749的前eqIdf458db68122849abb588feb2e682d9ac项和,是否存在常数eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c,对任意eqId532dc4d959024b79b546428f5856e5aa,使eqIdda67398536314f849f70ead102e67a25恒成立?若存在,求eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c取值范围;若不存在,说明理由.
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