已知()8,则展开式中系数绝对值最大项是第几项?并求出系数最大的项

已知()8,则展开式中系数绝对值最大项是第几项?并求出系数最大的项和系数最小的项.

答案

解析:设第r+1项系数的绝对值最大,则此项系数的绝对值必不小于它左、右相邻两项系数的绝对值.则有

5≤r≤6.

故系数绝对值最大项是第六项与第七项.

∵T6=(-1)5()3·()5

=-1 792

T7=(-1) 6()2·()6=1 792x-11

则系数最大项为1 792x-11,系数最小项为-1 792.

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