Question

Chứng tỏ rằng

\(\dfrac{1}{n^2}< \dfrac{1}{n-1}-\dfrac{1}{n}\) (nE\(N^X\), n>1)

Answer 1

\(n^2>n^2-n=n\left(n-1\right)\Rightarrow\dfrac{1}{n^2}< \dfrac{1}{n\left(n-1\right)}\Rightarrow\dfrac{1}{n^2}< \dfrac{1}{n-1}-\dfrac{1}{n}\)