名校
解题方法
1 . 已知
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0a244c1738103f33f722281fa9d57c.png)
A.![]() | B.此二项展开式系数最大的项为第4项 |
C.此二项展开式的二项式系数和为64 | D.![]() |
您最近一年使用:0次
名校
解题方法
2 . 在二项式
的展开式中,不正确的说法是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf68017d09f7fb8e16021785bdf8a2a.png)
A.常数项是第3项 | B.各项的系数和是1 |
C.偶数项的二项式系数和为32 | D.第4项的二项式系数最大 |
您最近一年使用:0次
2024-06-03更新
|
634次组卷
|
2卷引用:福建省晋江市第一中学2023-2024学年高二下学期期中考试数学试卷
名校
3 . 将三项式展开,得到下列等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d8c031e575939b5225a797fef26fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a070d714a0ef7ce6fc0efb304afb9a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7eb71feb75f1376909ba3c9be85101.png)
广义杨辉三角形
第
行 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
第
行
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
第
行
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
第
行
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
第
行
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
观察多项式系数之间的关系,可以仿照杨辉三角构造如图所示的广义杨辉三角形,其构造方法为:第
行为
,以下各行每个数是它正上方与左右两肩上的
个数
不足
个数时,缺少的数以
计
之和,第
行共有
个数
则关于
的多项式
的展开式中,
项的系数( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d8c031e575939b5225a797fef26fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a070d714a0ef7ce6fc0efb304afb9a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7eb71feb75f1376909ba3c9be85101.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5a3d4d8fa661dd7a09a9edcac9996a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5815a503758f95c613bbf3c2dd1df0.png)
广义杨辉三角形
第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be7581dbbccda50e5d5cd18056ddea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
观察多项式系数之间的关系,可以仿照杨辉三角构造如图所示的广义杨辉三角形,其构造方法为:第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394aee19f94c2b70fcce1d69b31dc7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1474532e151db068515ffb4ce75a2d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be56e9bad873ec62fa3319414edcdfd7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
4 .
展开式中常数项为12,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f8f91e28362304ad00aaf3cb03c3d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
您最近一年使用:0次
名校
解题方法
5 . 当
时,将三项式
展开,可得到如图所示的三项展开式和“广义杨辉三角形”:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ccb6deec8276b614f45fbbfc9e41be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b542111980fc8adc063f88005d08dd84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb2521d0d64b2308fa4da33c753e5912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5a339c13146f0fe62990b5cac1fe8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ae80be001f6b9fad16c828a7120f40.png)
...
的展开式中,
的系数为75,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ec1e39456a1ab2a93307e9b1652fd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ccb6deec8276b614f45fbbfc9e41be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b542111980fc8adc063f88005d08dd84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb2521d0d64b2308fa4da33c753e5912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5a339c13146f0fe62990b5cac1fe8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ae80be001f6b9fad16c828a7120f40.png)
...
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87c0fd8f1990b6de9cc2016bbf64d57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be56e9bad873ec62fa3319414edcdfd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.1 | B.![]() | C.2 | D.![]() |
您最近一年使用:0次
名校
解题方法
6 .
的展开式中,所有项的二项式系数和为____________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27fdb4e34d4fd497ad56e5bba8f5441d.png)
您最近一年使用:0次
名校
解题方法
7 . 在
的展开式中( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caed69925bbb651b770151ccc4fdb421.png)
A.所有奇数项的二项式系数的和为128 |
B.二项式系数最大的项为第5项 |
C.有理项共有两项 |
D.所有项的系数的和为![]() |
您最近一年使用:0次
2024-05-16更新
|
912次组卷
|
3卷引用:福建省泉州市安溪第一中学2023-2024学年高二下学期5月份质量检测数学试题
8 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33af6ba01682dcbd82f5826ad1ba864.png)
展开式中常数项是
,则
的值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33af6ba01682dcbd82f5826ad1ba864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9e571fb8fbf20e7ef8c89f195e6045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ce0336fa4640224bd9d812b11eb5cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.3 | B.4 | C.5 | D.6 |
您最近一年使用:0次
9 . 若
,则
的值为 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4074b25c83db80435d9854b3f6b3c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6f38cf5ea4954f5e2832efb987a930.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
10 . 关于
的展开式,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4206b668db768803942100b788d50743.png)
A.所有项的二项式系数和为64 | B.所有项的系数和为0 |
C.常数项为20 | D.系数最大的项为第4项 |
您最近一年使用:0次