Question

Chứng minh rằng :

1/n(n + 1) = 1/n - 1/n+1

MK ĐANG CẦN GẤP CÁC BN GIÚP MK NHA !!!!

Answer 1

Ta quy đồng :

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

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