1 . 如图,按照以下规律排列的数阵中,第i行从左向右第j个数记为
,如
,
,
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff0c0c8801acfcf827c2e381ce64fc6.png)
______ ;令
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7baacb324cd334db29b07dda412d8c61.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2b235520cf35bb35ca7ddb081f25c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d442e3ed65dd9a4181382ac3fee2ea5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07a509daa2e3c9b72149db3083b64f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591abf4a17a4ce26fbfbd39c833edc7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff0c0c8801acfcf827c2e381ce64fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a1e840aaf9a27e9836b37a413edd45a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7baacb324cd334db29b07dda412d8c61.png)
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899126226354176/2915735481704448/STEM/3c81d8e4-48bc-4be5-8aa3-3edc4a9ecae7.png?resizew=326)
您最近一年使用:0次
2022-02-13更新
|
719次组卷
|
6卷引用:山东省菏泽市2021-2022学年高二上学期期末数学试题
山东省菏泽市2021-2022学年高二上学期期末数学试题(已下线)技巧05 第二篇 解题技巧(测试卷)--第二篇 解题技巧篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》(已下线)第03讲 等比数列(核心考点讲与练)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)浙江省温州市瑞安市第六中学2021-2022学年高二下学期入学检测数学试题 .(已下线)专题11 数列前n项和的求法 微点10 数列前n项和的求法综合训练(已下线)高二上学期期末【压轴60题考点专练】(选修一+选修二)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)
2 . 欧拉函数
的函数值等于所有不超过正整数
,且与
互质的正整数的个数(公约数只有1的两个正整数称为互质整数),例如:
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6b32e6d479cb226c689b1368433f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea1d22420e844884025655b0893066e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39de1bc04496b97dcf401c669e6ab44e.png)
A.![]() | B.当![]() ![]() |
C.数列![]() | D.数列![]() ![]() ![]() |
您最近一年使用:0次
3 . 如图1,抛物线上任意两点连接所得的弦与抛物线围成一个弓形区域,求抛物线弓形区域的面积是古希腊数学家阿基米得最优美的成果之一,阿基米德的计算方法是:将弓形区域分割成无数个三角形,然后将所有三角形的面积加起来就可以得到弓形区域的面积.第一次分割,如图2,在弓形区域里以
为底边分割出一个三角形
,确保过顶点
的抛物线
的切线与底边
平行,
称为一级三角形;第二次分割,如图3,以
,两个边
,
为底边,在第一次分割得到的两个弓形区域继续分割出两个三角形
,
,确保过顶点
,
的抛物线
的切线分别与
,
平行,
,
都称为二级三角形;重复上述方法,继续分割新产生的弓形区域……,借助抛物线几何性质,阿基米德计算得出任意一级的所有三角形的面积都相等,且每个三角形的面积都是其上一级的一个三角形面积的
.设抛物线
的方程为
,直线
的方程为
,请你根据上述阿基米德的计算方法,求经过
次分割后得到的所有三角形面积之和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5f9ef971747d2d5bbc5823797a7a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5f9ef971747d2d5bbc5823797a7a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2aabebe28306cf8d00c803a95660c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ab9deecba8c0fb81cf93723df75ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3054c6616010df25fde222cf7e8020bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52c98c8ae04317175ad3b193722d0af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2aabebe28306cf8d00c803a95660c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ab9deecba8c0fb81cf93723df75ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a445bd4f12b6f325c2805ffd4ad0d49b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31c4f39399ec245a67db2933ed639f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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4 . 已知有穷数列
各项均不相等,将
的项从大到小重新排序后相应的序号构成新数列
,称数列
为数列
的序数列.例如数列
,
,
,满足
,则其序数列
为1,3,2.若有穷数列
满足
,
(n为正整数),且数列
的序数列单调递减,数列
的序数列单调递增,则下列正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c75058db8f3bce88c1ffd4eadf5f40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea6578afabc23f5d7041b88c3790dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c60c6b6f9416964c086506d8af41e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ae4e2547c5df93708a8a4e11ee399c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a1ed0b906a67310749d19e98662a53.png)
A.数列![]() |
B.数列![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
5 . 将
个数排成
行
列的数阵,如图所示:该数阵第一列的
个数从上到下构成以
为公差的等差数列,每一行的
个数从左到右构成以
为公比的等比数列(其中
0).已知
,记这
个数的和为
,下面叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4220a7e39a57c9467a9b17b96eff3de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1acee0663e9381923a9e0d9fe0c1809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31aa2af2c2cebc830d131ae8b812d15a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4220a7e39a57c9467a9b17b96eff3de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
6 . 已知数列
满足
(
为正整数),
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999ac8c1ef39251e07a7fc54cbf7e26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc73d432eb681f59489b833a7eab42e4.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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7 . 设
是数列1,
,
,…,
的各项和,
,
.
(1)设
,证明:
在
内有且只有一个零点;
(2)当
时,设存在一个与上述数列的首项、项数、末项都相同的等差数列,其各项和为
,比较
与
的大小,并说明理由;
(3)给出由公式
推导出公式
的一种方法如下:在公式
中两边求导得:
,所以
成立,请类比该方法,利用上述数列的末项
的二项展开式证明:
时
(其中
表示组合数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4706af45ba2b6dbe47eb4ef9653ce73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cd935d0f1d7ccab21b00591c6e93b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93daf697f42b3b3ad9fb5e2322d44a0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5f2b6c7baff8b8a78d4e9bf50645d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c64d8ccd22b77a2b30da084d30d2e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8226116fe4f4dbbb3f8d16ba6861c604.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3e5be1796493161a4df7e28a6f6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e229e9ebdef619bf6c33f5e206989431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f187754feb425947918104dcc262bb7.png)
(3)给出由公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cb17b07a5d34718ddb69311352f5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9124b5292f983cc4594dc5c83fd426d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cb17b07a5d34718ddb69311352f5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c918884347564b0969e53b797ea69e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9124b5292f983cc4594dc5c83fd426d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93daf697f42b3b3ad9fb5e2322d44a0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1fe01dcd9ae7ae33cb661205d3c427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c015bd3b114c45ca0881c8468b4b35d3.png)
您最近一年使用:0次
2020-06-23更新
|
1007次组卷
|
3卷引用:山东省潍坊市2020届高三6月高考模拟考试数学试题
8 . 已知红箱内有
个红球、
个白球,白箱内有
个红球、
个白球,所有小球大小、形状完全相同.第一次从红箱内取出一球后再放回去,第二次从与第一次取出的球颜色相同的箱子内取出--球,然后再放回去,依次类推,第
次从与第
次取出的球颜色相同的箱子内取出--球,然后:再放回去.记第
次取出的球是红球的概率为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
A.![]() |
B.![]() |
C.![]() |
D.对任意的![]() ![]() ![]() |
您最近一年使用:0次
9 . 对于正整数n,
是小于或等于n的正整数中与n互质的数的数目.函数
以其首名研究者欧拉命名,称为欧拉函数,又称为
函数,例如
,(10与1,3,7,9均互质)则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d40cb0f4dfbccdd4b6dadb06588fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d40cb0f4dfbccdd4b6dadb06588fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6969abc53fc2edb9ce770dbec4f1df06.png)
A.![]() | B.数列![]() |
C.若p为质数,则数列![]() | D.数列![]() ![]() |
您最近一年使用:0次
2022-12-29更新
|
366次组卷
|
2卷引用:山东省东营市胜利第一中学2021-2022学年高二上学期期末数学试题
10 . 某投资公司评估一个需要投资980万的项目,该项目从第1年年末开始,每一年的净利润是
万元,而且收益可以持续50年.若年利率为8%,记第
年年末的收益现值为
(
,
),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
___________ ;若该项目值得投资,则
的最小值为___________ 万元.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60a65136f3e00811ad1b401924fb10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4fdfde4a69599dbe9a97e83939e2ae.png)
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