Question

计算：（1-1/2的平方）*（1-1/3的平方）*（1-1/4的平方）.......（1-1/99的平方）*（1-1/100的平方）

每步有过程原因，好的+分

Answer 1

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

Answer 2

1/10201

Answer 3

平方差
=(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)
中间约分
=(1/2)(101/100)
=101/200