Question Number 158331 by HongKing last updated on 02/Nov/21
$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{n}}\:\left(\mathrm{n}\:+\:\mathrm{1}\right)}\:<\:\mathrm{2} \\ $$