杭州交通信息网水菜丽重口味:[急！！！]初一数学题
来源：百度文库 编辑：杭州交通信息网 时间：2024/05/03 05:51:01
[1-(1/2^2)][1-(1/3^2)][1-(1/4^2)]…[1-(1/100^2)]=?
原式＝(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/100)(1+1/100)
=1/2*3/2*2/3*4/3*……*99/100*101/100
=1/2*101/100
=101/200
[1-(1/2^2)][1-(1/3^2)][1-(1/4^2)]…[1-(1/100^2)]
=[1^2-(1/2)^2]*[1^2-(1/3)^2]*...[1^2-(1/100)^2]
=(1-1/2)^2*(1-1/3)^2*...(1-1/100)^2
=(1/2)^2*(2/3)^2*...(99/100)^2
=(1/2*2/3*3/4*...98/99*99/100)^2
=(1/100)^2
=1/10000