1 . 若
的展开式中
的系数为20,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4753f4a4456d0df13843b71015bfa14.png)
_____ ;展开式中的常数项为______ (用含
或
的代数表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2598a9ccad9ca7a3454ac57129e5a34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d800f03de80068a1172beac3a2c75587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4753f4a4456d0df13843b71015bfa14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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解题方法
2 . 设
,其中
为实数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74be0e395883f9cb867b4ab11e21080.png)
__________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1268d06d6586e3dce88277a12a21dd91.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eeddf70992c775c3766ceba3b870999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fb4cf459841e547e2d358d392abc0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74be0e395883f9cb867b4ab11e21080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1268d06d6586e3dce88277a12a21dd91.png)
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3 .
展开式中常数项是_______ ,最大的系数是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/954d1d4055102a2362232581817264dd.png)
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解题方法
4 . 已知
展开式的二项式系数和为64,则其展开式中含
的项是_____ ;各项系数的绝对值和是_____ (用数字作答).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d97e331d84f00eed9c8b61cb9c1fbe8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d800f03de80068a1172beac3a2c75587.png)
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解题方法
5 .
的展开式中各项系数的和为
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
______ ,该展开式中常数项为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2ff2b617cb560ac7f03d28f7bae1ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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6 . 若
展开式中前三项的系数成等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
_________ ,含
的项为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d71bd3fba4f3761ba54253ff018829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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解题方法
7 . 已知二项式
的展开式中的第2项为常数项,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
____________ ,二项展开式中所有项的系数和为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2733b8e5e7750d650c5a6f24bc2afb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
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8 . 在二项式
的展开式中,已知第4项的二项式系数为20,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
_____ ,
的系数为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51fef79b0f659dd8a6cb1b163067abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d800f03de80068a1172beac3a2c75587.png)
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9 . 若二项式
的展开式中存在常数项,则正整数n的最小值为________ ;当正整数n取最小值时,二项式
的展开式中的常数项为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3b8f5452596907b5351ca5f4bb917e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3b8f5452596907b5351ca5f4bb917e.png)
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10 . 若
的展开式中有常数项,则
的最小值为______ ,当
取最小值时,
的展开式中的常数项是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb99ee443234be0e46361c04b6534754.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/eb99ee443234be0e46361c04b6534754.png)
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