3

Part of 2020 Latvia Baltic Way TST

Problems(1)

Similar to harmonic series, but with 2020

Source: Latvian TST for Baltic Way 2020 P3

Prove that for all positive integers

n

the following inequality holds:

\frac{1}{1^2 +2020}+\frac{1}{2^2+2020} + \ldots + \frac{1}{n^2+2020} < \frac{1}{22}