这题数学题怎么做(1+1/2)(1+1/3)(1+1/4)...(1+1/2010)（1/2-1)(1/3-1)(1/4-1)...(1/2011-1)

题目

这题数学题怎么做(1+1/2)(1+1/3)(1+1/4)...(1+1/2010)（1/2-1)(1/3-1)(1/4-1)...(1/2011-1)
十二点以前解答出,

答案

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