Question

Chứng minh rằng 

\(\dfrac{1}{n.\left(n+1\right)}=\dfrac{1}{n}-\dfrac{1}{n+1}\left(nEN^{\cdot}\right)\)

Answer 1

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

Answer 2

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