Question

hãy chứng minh rằng:

\(\frac{1}{n.\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}vớin\in Nsao\)

Answer 1

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

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

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

Answer 2

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