分解一下将1/n(n+1)分解成1/n - 1/(n+1)所以题目=1/1-1/2+1/2-1/3+1/3-1/4...+1/99-1/100=1-1/100=99/100
拆项相消法1/n(n+1)=1/n-1/(n+1)1/n(n+k)=1/k[1/n-1/(n+k)]原式=1/1-1/2+1/2-1/3+1/3-1/4...+1/99-1/100=1-1/100=99/100
