Question

Chứng minh đẳng thức:

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

Answer 1

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

Vì \(\dfrac{1}{n}-\dfrac{1}{n+1}=\dfrac{1}{n}-\dfrac{1}{n+1}\)

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

Answer 2

Chứng minh

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

Ta có:VP=\(\dfrac{1}{n}-\dfrac{1}{n+1}\)=

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

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