在如图所示的数阵中,第
行从左到右第3个数是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
![](https://img.xkw.com/dksih/QBM/2011/3/28/1570067954016256/1570067959275520/STEM/2e9bbd1d7ce44ee6ab57afa3053a845b.png?resizew=164)
10-11高二下·河南许昌·期末 查看更多[1]
(已下线)2010-2011年河南省许昌市高二下学期联考数学文卷
更新时间:2016-11-30 16:14:21
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填空题-单空题
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适中
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【推荐1】已知数列
满足
,且
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf9ee81d38182ecd57b0777f910aa65.png)
___________ .(结果用含a的式子表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f03b007be99a17613246b5ea1ff86d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e39a28754dce79f732da5f5585a86ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/739999abba91227d93267602e0ebe9f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf9ee81d38182ecd57b0777f910aa65.png)
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【推荐2】数列
的前n项和是
,若数列
的各项按如下规则排列:
有如下运算和结论:
①
;
②
;
③数列
,
,
,
,…是等比数列;
④数列
,
,
,
,…的前n项和
;
⑤若存在正整数k,使
,则
.
在横线上填写出所有你认为是正确的运算结果或结论的序号________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7946b20669aec5060b4229086a477316.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a140699aa48bbe6ce03833c4434bac.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e62963508712b6782f8d5101296187.png)
③数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2466735503515350fb346f469ecc30b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0151a2e204a0664939cb6cb3a5242e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1fcff7f96b0c2c95cd646ad04dc4232.png)
④数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2466735503515350fb346f469ecc30b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0151a2e204a0664939cb6cb3a5242e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1fcff7f96b0c2c95cd646ad04dc4232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a6d72db96302e3dd395a2f58e7f4c22.png)
⑤若存在正整数k,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b762efc9157017b74c2306b2b56c1198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05cb38daf06c2adeca7841ff3de9d125.png)
在横线上填写出所有你认为是正确的运算结果或结论的序号
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名校
【推荐1】设n为正整数,f(n)=1+
+
+…+
,计算得f(2)=
,f(4)>2,f(8)>
,f(16)>3,观察上述结果,可推测一般的结论为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6a2eba56d4f2d1670b0256b8d86b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
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解题方法
【推荐2】对于有
个数的序列
,
,
,
,实施变换
得新序列
,
,
,
,记作
;对
继续实施变换
得新序列
,记作
;
,
.最后得到的序列
只有一个数,记作
.
(1)若序列
为
,
,
,
,则序列
为__________ .
(2)若序列
为
,
,
,
,则序列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412f8bf729bbe22fc47152842301fa08.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e337c6cc4f4b7e125008ec1d97df72e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02755c052027a522c45a9c54b9e5fa57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67328d77bc68c06267a9124a0e0c22c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9d2e152db0845ff23e4ea0cd00974d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d32b729bfccc73de23d70a293db435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78c6585d2d40c09d618f787dd4f1cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384ea3cfcbf90803bd91ad0bc6ad52e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1e52bc14127c91c5c0bb9ec7f14905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19eaf1766da2b5730e0f933fdcd14633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ea50db79b18d8700cfa2559ff5e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16801cc4a7c851642216e8cfe47e4643.png)
(1)若序列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
(2)若序列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412f8bf729bbe22fc47152842301fa08.png)
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