解题方法
1 . 已知
为数列
的前
项和,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b83c5596cc2dbeb14988696db3136d.png)
________
![](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/f20c98ff12e3d272ef58b106b8b68dbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b83c5596cc2dbeb14988696db3136d.png)
您最近一年使用:0次
名校
解题方法
2 . 已知数列
为等比数列,
是它的前
项和,若
,且
与
的等差中项为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec66faf5ace112f012aa331efa5c82f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a47bf269ab9edd83336b48f05d9f4ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59ab85c075a09d55d69e159e4abb268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
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2020-04-10更新
|
1148次组卷
|
3卷引用:广东省广州市第六中学2018-2019学年高三上学期期中数学(文)试题
广东省广州市第六中学2018-2019学年高三上学期期中数学(文)试题黑龙江省佳木斯市第一中学2019-2020学年高一下学期第一学段考试文科数学试题(已下线)专题01 《数列》中的典型题-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)
解题方法
3 . 已知数列
的前
项和为
,且
,则数列
的则前
项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.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/c8370a173854471a3eb27637993a3d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75b3c14179d05f8237f184dad3f87ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
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2024-05-27更新
|
392次组卷
|
2卷引用:陕西省部分学校(菁师联盟)2024届高三下学期5月份高考适应性考试理科数学试题
2024·全国·模拟预测
解题方法
4 . 已知正项数列
的前
项和为
,
,若存在非零常数
,使得
对任意的正整数
均成立,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
______ ,
的最小值为______ .
![](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/22c5c4ac959eb2c4b74afabc9cdd3a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a878f130126507f5d1f6524c136a6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b61a2436af7a7b8daddfb2f17fe8d.png)
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5 . 第二十四届北京冬奥会开幕式上由96片小雪花组成的大雪花惊艳了全世界,数学中也有一朵英丽的雪花————“科赫雪花”. 它的绘制规则是:任意画一个正三角形
,并把每一条边三等分, 以三等分后的每边的中间一段为边向外作正三角形,并把这“中间一段”擦掉,形成雪花曲线
,重复上述两步, 画出更小的三角形,一直重复,直到无穷,形成雪花曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56e7f3a47ece14e1c10a5f1a12946ea.png)
设雪花曲线
周长为
,面积为
,若
的边长为1,则
=_______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56e7f3a47ece14e1c10a5f1a12946ea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/dce610b9-9435-4955-8951-47fa025d51b4.png?resizew=310)
设雪花曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7c5e7bd6bac51402ffa04b4144ec78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2813ee8f26cca880b6427f5f545d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
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6 . 在数列
中,
.若对任意的
,不等式
恒成立,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ef1e5adfc8af1c985ba20bb1fb84bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ea8a9555430aa4504b6e3e6229d11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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解题方法
7 . 螺旋线这个名词来源于希腊文,它的原意是“旋卷”或“缠卷”,平面螺旋便是以一个固定点开始向外逐圈旋烧而形成的曲线,如图甲所示.如图乙所示阴影部分也是一个美丽的螺旋线型的图案,它的画法是这样的:正方形ABCD的边长为4,取正方形ABCD各边的四等分点E,F、G,H,作第2个正方形EFGH,然后再取正方形EFGH各边的四等分点M,N,P,Q,作第3个正方形MNPQ,依此方法一直继续下去,就可以得到阴影部分的图案,设正方形ABCD的边长为
,后续各正方形的边长依次为
;如图乙阴影部分,直角三角形AEH的面积为
,后续各直角三角形的面积依次为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7e11b0305b50afb2d0605804c8de97.png)
___ ;记数列
的前n项和为
,若对于
恒成立,则
的最大值为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72f109aceda27a70c12a6a8769b58c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b8d52591c3161797e66356a3a9f3cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7e11b0305b50afb2d0605804c8de97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558345396c4db9c05eb41814e2158748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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8 . 已知数列
的前n项和为
.且
,
是公差为
的等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b1ebe94ad16d80a21f7aa20b59458a.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90207deac50fb1606529b49047f990f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47beab88f3c7978932f2e13824d60191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b1ebe94ad16d80a21f7aa20b59458a.png)
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2021-04-01更新
|
753次组卷
|
4卷引用:广西2021届高三综合能力测试(CAT)(一)3月联考数学(文)试题
广西2021届高三综合能力测试(CAT)(一)3月联考数学(文)试题广西柳州市2021届高三下学期三模数学(文)试题广西柳州市2021届高三下学期三模数学(理)试题(已下线)专题09 数列的通项公式、数列求和及综合应用(练习)-1
解题方法
9 . 英国著名物理学家牛顿用“作切线”的方法求函数零点.已知二次函数
有两个不相等的实根b,c,其中
.在函数
图象上横坐标为
的点处作曲线
的切线,切线与x轴交点的横坐标为
;用
代替
,重复以上的过程得到
;一直下去,得到数列
,记
,且
,
,则数列
的前n项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b2139fd92090785e08fbdf814c41f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2414f9aa6d06243ccd076093bb3856d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ab44c68cb5ca9cc745e230f0b3aa2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c417392924cccaaf58cfaf5eb48a1864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
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名校
解题方法
10 . 已知数列
的首项为1,在
展开式中,若
为公差为2的等差数列,展开式中
的系数为______ ;若
为公比为2的等比数列,展开式中
的系数为______ .(用数字作答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d38876601e02bdb2398fe14ee35d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af9764aa29ce1378f9c6f6c3ceea928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3336c8ed5361c10c37300e41e03f9f2f.png)
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