Question

Chứng tỏ rằng với n\(\in\) N,n\(\ne\)0 thì:

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

Answer 1

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

Vậy n\(\in\) N và n\(\ne\) 0

Answer 2

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

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

Đúng nha Speed Ninja