解题方法
1 . 已知各项均为正数的数列
的前n项和满足
,且
.
(1)求
的通项公式:
(2)设数列
满足
,并记
为
的前n项和,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c3f4f76c7bde482ebcaaab4bb59b0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015a269200ae193657d55f61e8b0bfda.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742721845dbe4fcc82018b6ae15906ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a971a32e733960283abc7396bfc23912.png)
您最近一年使用:0次
2020-12-01更新
|
1444次组卷
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6卷引用:天津市北辰区2020届高三上学期第一次联考(期中)数学试题
天津市北辰区2020届高三上学期第一次联考(期中)数学试题2020届浙江省杭州市建人高复高三下学期4月模拟测试数学试题(已下线)考点20 数列的综合运用-2021年高考数学三年真题与两年模拟考点分类解读(新高考地区专用)浙江省杭州市建人高复学校2020届高三下学期5月模拟数学试题(已下线)专题9 数列通项公式和前n项和-2021年高考冲刺之二轮专题精讲精析(已下线)专题11 数列前n项和的求法 微点9 转化化归法求和
解题方法
2 . 已知有穷数列
共有
项(整数
),首项
,设该数列的前
项和为
,且
,其中常数
.
(Ⅰ)求证:数列
为等比数列;
(Ⅱ)若
,数列
满足
,求
的和(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5631bc01b998a4b3fabd9e131699dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeaed9ec21e090defafcfeefe0059c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.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/921101da86f17e4f4b6d254ca51fde3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
(Ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57def6b0c89b6f806344696963162289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a81a4d5c42a5fe3aa2fe43774bcafac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da5be3f28f79bf2b371ef4592b998ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
3 . 已知数列
是首项为1的等差数列,数列
是公比不为1的等比数列,且满足
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dbe8fa82ab04f0a4ba4ad1c570c9aa1.png)
(1)求数列
,
的通项公式;
(2)令
,记数列
的前n项和为
,求证:对任意的
,都有
;
(3)若数列
满足
,
,记
,是否存在整数
,使得对任意的
都有
成立?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039271f3111b0e21bc1282fcc22cf016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84672a737e1ba65228ffd2f0064a8c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40751e69baead4a0d5bea384aedfa6c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dbe8fa82ab04f0a4ba4ad1c570c9aa1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039271f3111b0e21bc1282fcc22cf016.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c442b01e6f3190aa64b3cb1810212a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082dd35c1eebe15ec8d8b060f28cfd98.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea6578afabc23f5d7041b88c3790dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614bac93e838d86d18422bed438368df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328d9e6ef9823fd2744d553ffb6ac99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfc635d85ba1a671159602cdba4c276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2020-07-09更新
|
970次组卷
|
2卷引用:江苏省泰州中学2020届高三下学期第五次模拟考试数学试题
名校
4 . 已知数列
中,
,
.
(1)求证:数列
是等比数列;
(2)求数列
的前
项和
,并求满足
的所有正整数
.
![](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/4716ec121ba18b4511210c1a549f9cc6.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c3083c9192f3a3e1476d9f555eb923.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49763402b2f2023f0ba64c37924267d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2018-05-24更新
|
1753次组卷
|
10卷引用:【全国百强校】天津市第一中学2018届高三下学期第五次月考数学(理)试题
【全国百强校】天津市第一中学2018届高三下学期第五次月考数学(理)试题天津市南开中学2019-2020学年高三上学期12月月考数学试题2015届山东省日照市高三3月模拟考试理科数学试卷2015届湖南长沙长郡中学等十三校高三第二次联考理科数学试卷2015届广东省汕头市潮南区高三高考模拟二理科数学试卷2015届浙江省杭州二中高三仿真考理科数学试卷2015-2016学年黑龙江省鹤岗一中高一下期中理科数学试卷黑龙江省穆棱市第一中学2016-2017学年高一下学期期中考试数学试题【全国百强校】河北省衡水中学2017-2018学年高一下学期期末模拟数学试题2019届浙江省慈溪中学高三下学期高考适应性测试数学试题
名校
5 . 已知曲线
:
,
:
(
),从
上的点
作
轴的垂线,交
于点
,再从点
作
轴的垂线,交
于点
.设
,
,
.
(Ⅰ)求数列
的通项公式;
(Ⅱ)记
,数列
的前
项和为
,求证:
;
(Ⅲ)若已知
(
),记数列
的前
项和为
,数列
的前
项和为
,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe49779f2db4a075d3241052eb87d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683a5650801fecc69a0244ab65044cd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d947908a767ea6af0aa03c7a90705cd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36caec2e0dfbf9f4cf732c4b5fd1c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c775fc62e7696028a9184e5212f0446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b394d4db69cf69f8d8058898298efd3d.png)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
(Ⅱ)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385770d258713f3a9d86bc0ed576277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e54215133ebab7c582b676cf68d1677.png)
(Ⅲ)若已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c688ab7ea6f71d5695361053d46b256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3cdf1d28efbaf1e8aaf8e2be4636fa5.png)
您最近一年使用:0次
6 . 已知数列
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694d9d408cec688e8c8a13e4868a5deb.png)
(I)求证:数列
是等比数列
(II)求数列
的通项公式
(III)设
,若
,使
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694d9d408cec688e8c8a13e4868a5deb.png)
(I)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6631307e8ff61b215f447f2527c36e04.png)
(II)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(III)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9dfeeff5b7c543226a16dac4509375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23487d83aa14650649f1e0b636acabb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6143b63cb006d60ffb578a90da8f9f5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2017-12-11更新
|
3790次组卷
|
11卷引用:2016届天津市和平区高三第四次模拟理科数学试卷
2016届天津市和平区高三第四次模拟理科数学试卷2016届天津市和平区高三第四次模拟文科数学试卷天津市第一中学2018届高三上学期第二次月考数学(文)试题四川省泸州市泸县第四中学2019-2020学年高一下学期第四学月考试数学试题(已下线)专题32 数列大题解题模板-2021年高考一轮数学(文)单元复习一遍过(已下线)专题32 数列大题解题模板-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)专题32 数列大题解题模板-2021年高考一轮数学(理)单元复习一遍过湖北省黄冈市黄梅国际育才高级中学2019-2020学年高一下学期复学考试数学试题(已下线)专题03 数列大题解题模板-2020-2021学年高二数学单元复习(人教A版选择性必修第二册)江苏省盐城市伍佑中学2022-2023学年高三上学期12月月考数学试题(已下线)专题11 数列前n项和的求法 微点4 裂项相消法求和(二)
名校
7 . 已知数列
满足
,且
.
(1)求
的通项公式;
(2)设
,求数列
的前
项和
;
(3)设
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df10b245bd0b282113045f2c35e0ef44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a174b926e412de33ae67e13324e1f6c9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8c8216298ccd6560d601f67c8ea3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212b97a1d6785f21e8559809efc0ea47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5dcd4dc278a8ece638d0c8660b6cea.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085f5ef478b4fe1174056f38b51e9131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56106c358f1d9dc113d7030fb5fa5696.png)
您最近一年使用:0次
2017-12-11更新
|
2447次组卷
|
2卷引用:天津市第一中学2018届高三上学期第二次月考数学(理)试题
8 . 设数列{an}满足:a1=1,an+1=3an,n∈N*.设Sn为数列{bn}的前n项和,已知b1≠0,
2bn–b1=S1•Sn,n∈N*.
(Ⅰ)求数列{an},{bn}的通项公式;
(Ⅱ)设
,求数列{cn}的前n项和Tn;
(Ⅲ)证明:对任意n∈N*且n≥2,有
+
+…+
<
.
2bn–b1=S1•Sn,n∈N*.
(Ⅰ)求数列{an},{bn}的通项公式;
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba66ef1e765632f1f62a896a55345ec0.png)
(Ⅲ)证明:对任意n∈N*且n≥2,有
![](https://img.xkw.com/dksih/QBM/2016/4/6/1578863833063424/1578863833587712/STEM/5cbea60fcd9a41df820c1348be5fb289.png)
![](https://img.xkw.com/dksih/QBM/2016/4/6/1578863833063424/1578863833587712/STEM/cd58906f007c4bbb91a3c58d0302b741.png)
![](https://img.xkw.com/dksih/QBM/2016/4/6/1578863833063424/1578863833587712/STEM/7b9080738c67409fa6e3b7faba7dfb8d.png)
![](https://img.xkw.com/dksih/QBM/2016/4/6/1578863833063424/1578863833587712/STEM/acf6c460768a40beaf739da22cdbf90a.png)
您最近一年使用:0次
2016-12-03更新
|
1614次组卷
|
4卷引用:2015届天津市南开区高三一模理科数学试卷
9 . 已知数列{an}与{bn}满足bn+1an+bnan+1=(﹣2)n+1,bn=
,n∈N*,且a1=2.
(1)求a2,a3的值
(2)设cn=a2n+1﹣a2n﹣1,n∈N*,证明{cn}是等比数列
(3)设Sn为{an}的前n项和,证明
+
+…+
+
≤n﹣
(n∈N*)
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759012970496/1571759018713088/STEM/b8eb63c30ed740169eae93d38e4d96d5.png)
(1)求a2,a3的值
(2)设cn=a2n+1﹣a2n﹣1,n∈N*,证明{cn}是等比数列
(3)设Sn为{an}的前n项和,证明
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759012970496/1571759018713088/STEM/e13d541dd0f14d58a6a6f3108d16dca7.png)
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759012970496/1571759018713088/STEM/6ade77d0938046bbaaf003583813230f.png)
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759012970496/1571759018713088/STEM/03ad00b5caee4419bc1a91309f2b515b.png)
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759012970496/1571759018713088/STEM/49f9c22db34c43a48a1ff7291cce194a.png)
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571759012970496/1571759018713088/STEM/e6eab64ac68d49c7973ccb42186ca003.png)
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真题
10 . 在数列
与
中,
,数列
的前
项和
满足
,
为
与
的等比中项,
.
(Ⅰ)求
的值;
(Ⅱ)求数列
与
的通项公式;
(Ⅲ)设
.证明
.
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/813be1cf542c45798e71fdc7ba882344.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/0b1f298ceb954a558ea1f4fad3f29af0.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/548ebffc86384a838d27814ae64fc871.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/813be1cf542c45798e71fdc7ba882344.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/a38d1b920aec483c96206d43eee90ac4.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/7a676c7243304dfdb9036b8769b2a157.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/1d0f16dc5a4f41d3adf5f484b898c9f2.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/be312a87633e46cf81335e2fc434e3db.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/b864f3e861b5427aa2be157dbb8a4e60.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/4348208411b44f8189ae0182150f73a9.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/c70e00a82c7a45f09ba87c7ab1646276.png)
(Ⅰ)求
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/e9b838c4e6534ea69e1262eb353cf9af.png)
(Ⅱ)求数列
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/813be1cf542c45798e71fdc7ba882344.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/0b1f298ceb954a558ea1f4fad3f29af0.png)
(Ⅲ)设
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/e32a4e148ded498aa8086a9b5eff70e9.png)
![](https://img.xkw.com/dksih/QBM/2010/4/1/1569688487706624/1569688630157312/STEM/fc145be6d0fe45cba96e4235a4dc4739.png)
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