Question

（1-2²分之一）（1-3²分之一）×.×（1-100²分之一） 计算!

Answer 1

原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/99)(1+1/99)(1-1/100)(1+1/100)

=(1/2)[(3/2)(2/3)(4/3)(3/4)(5/4).(98/99)(100/99)(99/100)](101/100)

=(1/2)*1*1*1.*1*(101/100)

=(1/2)(101/100)

=101/200