Question

[ha nguyen thi]

chứng minh : 1/ n (n+1) (n+2) =  1/ 2 ( 1/ n(n+1)  -  1/(n+1 ) (n+2) )

Answer 1

[Nguyễn Việt Lâm]

\(\dfrac{1}{n\left(n+1\right)\left(n+2\right)}=\dfrac{2}{2n\left(n+1\right)\left(n+2\right)}=\dfrac{\left(n+2\right)-n}{2n\left(n+1\right)\left(n+2\right)}\)

\(=\dfrac{n+2}{2n\left(n+1\right)\left(n+2\right)}-\dfrac{n}{2n\left(n+1\right)\left(n+2\right)}=\dfrac{1}{2}\left[\dfrac{1}{n\left(n+1\right)}-\dfrac{1}{\left(n+1\right)\left(n+2\right)}\right]\)