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National and Regional Contests
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Latvia BW TST
2020 Latvia Baltic Way TST
3
Similar to harmonic series, but with 2020
Similar to harmonic series, but with 2020
Source: Latvian TST for Baltic Way 2020 P3
October 17, 2020
inequalities
Problem Statement
Prove that for all positive integers
n
n
n
the following inequality holds:
1
1
2
+
2020
+
1
2
2
+
2020
+
…
+
1
n
2
+
2020
<
1
22
\frac{1}{1^2 +2020}+\frac{1}{2^2+2020} + \ldots + \frac{1}{n^2+2020} < \frac{1}{22}
1
2
+
2020
1
+
2
2
+
2020
1
+
…
+
n
2
+
2020
1
<
22
1
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