chuột cống

\(\frac{1}{n}-\frac{1}{n+1}=\frac{n+1}{n\left(n+1\right)}-\frac{n}{n+1}=\frac{\left(n+1\right)-n}{n\left(n+1\right)}=\frac{1}{n\left(n+1\right)}\)

Vậy \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)