计算(1-1/(2^2)(1-1/(3^2)(1-1/(4^2)…(1-1/(100^2)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 07:56:05
计算(1-1/(2^2)(1-1/(3^2)(1-1/(4^2)…(1-1/(100^2)

计算(1-1/(2^2)(1-1/(3^2)(1-1/(4^2)…(1-1/(100^2)
计算(1-1/(2^2)(1-1/(3^2)(1-1/(4^2)…(1-1/(100^2)

计算(1-1/(2^2)(1-1/(3^2)(1-1/(4^2)…(1-1/(100^2)
(1-1/2^2)(1-1/3^2)(1-1/4^2)*.*(1-1/100^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)*.*(1-1/100)(1+1/100)
=1/2*3/2*2/3*4/3*3/4*5/4*.*99/100*101/100
=1/2*101/100
=101/200