1 . 在
的展开式中,各奇数项的二项式系数之和为32,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a43d72a9b8300b61a7f7491ef7f04a3.png)
A.常数项为![]() | B.![]() |
C.![]() | D.![]() ![]() |
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2 . 在
的展开式中,下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1ec77f711155521c235e226a4615f5.png)
A.二项式系数之和为64 | B.各项系数之和为![]() |
C.二项式系数最大的项为![]() | D.常数项为![]() |
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3 .
的展开式中
项的系数为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2cef315592e08c4718f3fadd3e37b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
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4 . 若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc41a964cee9cff69c3b805afd29f086.png)
______ .(用数字作答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae28d359458e5dbe832fef4a737cf6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc41a964cee9cff69c3b805afd29f086.png)
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5 .
的展开式中
的系数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f701dfca9ec850885b9d9488582d72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e2bd69747a7a90b575e97e2914aea4.png)
A.48 | B.-48 | C.72 | D.-72 |
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6 . 英国数学家泰勒(B.Taylor,1685—1731)发现了:当函数
在定义域内n阶可导,则有如下公式:
以上公式称为函数
的泰勒展开式,简称为泰勒公式.其中,
,
表示
的n阶导数,即
连续求n次导数.根据以上信息,并结合高中所学的数学知识,解决如下问题:
(1)写出
的泰勒展开式(至少有5项);
(2)设
,若
是
的极小值点,求实数a的取值范围;
(3)若
,k为正整数,求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ba62322394a513a9e60536e424f112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c875ad8fafc41d5c82baf23bb5e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd370c3b127fbdb77b6e5c40318328d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad040ae0fab73f5dd7b1af48cd3b5f93.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a923c6ef8e8a289acf935ca73c92a28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf90a3d768f2a8ff0ede2f973d1dad1.png)
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2024-06-04更新
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2卷引用:贵州省遵义市2024届高三第三次质量监测数学试卷
7 . 若
的展开式中x的系数为21,则n的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654fa7b013ef33fff5441879c5e547b0.png)
A.8 | B.7 | C.6 | D.5 |
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8 .
的展开式的二项式系数和为1024,则展开式的各项系数和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e97a55fecff2e9affe29c5e30ec86c1.png)
A.![]() | B.1 | C.![]() | D.![]() |
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9 . 二项式
的展开式中仅有第5项系数最大,则
的展开式中x的系数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c12176dbc04f873ef140125f2511bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f37b622db0d41b42f9f085f43a011969.png)
A.![]() | B.![]() | C.28 | D.56 |
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2024-05-20更新
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463次组卷
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2卷引用:贵州省遵义市2023-2024学年高二下学期5月期中联考数学试题
10 . 若给定一个数列
,其连续两项之差构成一个新数列:
,
,
,…,
,…,这个数列称为原数列
的“一阶差数列”,记为
,其中
.再由
的连续两项的差得到新数列
,
,
,…,
,…,此数列称为原数列
的“二阶差数列”,记为
,其中
.以此类推,可得到
的“p阶差数列”.如果数列
的“p阶差数列”是非零常数数列,则称
为“p阶等差数列”.
(1)证明由完全立方数
组成的数列
是“3阶等差数列”;
(2)若
(
且
,
),证明数列
是“k阶等差数列”,并且若将
的“k阶差数列”记作
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe164d8a8a4049e01565b576007651de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01416ee1d48b17f889e444b7eda99740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffdd0f523e96587d0e42d41151a3f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fcde3a21ad686b1befcaefea2b6f5b.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/e5653b60d16ec4e653518f0562680250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45aec1e4ca31a14444f4bc8682ab5d9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085a37c2996e097b38235498876dadbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50a9f25dce1e2d1cb2858964e46b70c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a236ab883a88dc0d034f3ad6c0e4adfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703cdc7668aa4dcab77e448249f9446a.png)
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)证明由完全立方数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0d016a383115a90050f6af28b22bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c11de1cc7764942724e0d08a826a294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835c74bbb8c61dd2d2f008664a8c8810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232d1ce3ad14256b1543e6007ff1675d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](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/4c3f801c87c837385eca80c706e8adae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f6c0bb6318dd2a8c33bd76697bce874.png)
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