:计算(1-1/2的二次方)(1-1/3的三次方)...(1-1/9的九次方)(1-1/10的十次方)

问题描述:

:计算(1-1/2的二次方)(1-1/3的三次方)...(1-1/9的九次方)(1-1/10的十次方)

11/20

(1-1/2的二次方)(1-1/3的三次方)...(1-1/9的九次方)(1-1/10的十次方)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)....(1-1/9)(1+1/9)(1-1/10)(1+1/10)
=1/2*3/2*2/3*4/3*...*8/9*10/9*9/10*11/10
=1/2*11/10
=11/20

用平方差
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/10)(1+1/10)
=(1/2)(3/2)(2/3)(4/3)……(9/10)(11/10)
中间约分
=(1/2)(11/10)
=11/20