1/(1*2)+1/(2*3)+1/(3*4)+…+1/(n*(n+1))的计算公式

题目

1/(1*2)+1/(2*3)+1/(3*4)+…+1/(n*(n+1))的计算公式

答案

1/1*2+1/2*3+1/3*4+1/4*5+...+1/n*[n+1]
=1/1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/n+1
=1/1-1/n+1
=n/(n+1)