1/(1×3)+1/(3×5)+1/(5×7)+...+1/(2009×2011)
=(1/2)(1-1/3+1/3-1/5+1/5-1/7+...+1/2009-1/2011)
=(1/2)(1-1/2011)
=1005/2011
一般的：
1/[n(n+1)]=1/n -1/(n+1)
1/[n(n+2)]=(1/2)[1/n -1/(n+2)]
…………
1/[n(n+k)]=(1/k)[1/n -1/(n+k)]