Page 1 of 1

Double inequality

Posted: Thu Nov 10, 2016 4:36 pm
by Papapetros Vaggelis
If \(\displaystyle{n\in\mathbb{N}\,,n\geq 2}\), then prove that

\(\displaystyle{n\,\left(\sqrt[n]{n+1}-1\right)<\sum_{k=1}^{n}\dfrac{1}{k}<n\,\left(1-\dfrac{1}{\sqrt[n]{n+1}}+\dfrac{1}{n+1}\right)}\).