计算(1/2-1)×(1/3-1)×（1/3-1）×（1/4-1）×.×（1/2010-1）×(1/2011-1)等于多少?

题目

计算(1/2-1)×(1/3-1)×（1/3-1）×（1/4-1）×.×（1/2010-1）×(1/2011-1)等于多少?

答案

(1/2-1)×(1/3-1)×(1/4-1)×...×(1/2011-1)
=(1-1/2)(1-1/3)(1-1/4)...(1-1/2011)
=(1/2)(2/3)(3/4)...(2010/2011)
=(1×2×3×...×2010)/(2×3×4×...×2011)
=1/2011