Prove that $\sum_{n=1}^{2022^{2022}} \frac{1}{\sqrt{n^3+2n^2+n}}<\frac{19}{10}$.
Problem
Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade
Tags: algebra, Inequality, Sum
Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade
Tags: algebra, Inequality, Sum
Prove that $\sum_{n=1}^{2022^{2022}} \frac{1}{\sqrt{n^3+2n^2+n}}<\frac{19}{10}$.