1/1x5+1/5x9+1/9x13+……+1/25x29

1/(1×5)+1/(5×9)+...+1/(25×29) =(1/4)(1-1/5+1/5-1/9+...+1/25-1/29) =(1/4)(1-1/29) =(1/4)(28/29) =7/29 一般的对于正整数n，k 1/[n(n+k)]=(1/k)[1/n -1/(n+k)]