1-1/n^2=(1+1/n)(1-1/n)=(n+1)/n乘(n-1)/n
设n=2
原式等于[ (n+1)(n-1)(n+1+1)(n+1-1)......(n+2007)(n+2006]/ nn(n+1)(n+1)....(n+2006)(n+2006)
分式上下相等的约去, 则结果等于 (n-1)(n+2007)/[n(n+2006)]
2009/(2x2008)=2009/4016
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/2008)(1+1/2008)
=1/2 × 3/2×2/3 × 4/3×3/4 × ……×2008/2007×2007/2008 ×2009/2008
=1/2×2009/2008
=2009/4016
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