根据公式a^2-b^2=(a-b)(a+b),得：
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)...(99/100)(101/100)
=[(1/2)(2/3)(3/4)...(1-1/99)(99/100)]×[(3/2)(4/3)(5/4)...(1+1/99)(101/100)]
=(1/100)(101/2)
=101/200