MathCS.org - Real Analysis: Examples 4.2.12(b):

Theorem 4.2.11: p Series

The series

converges.

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We will use the comparison test, together with the p-series test. First, note that

1 / (1 + n ²) < 1 / n ²

But since the series 1 / n ² is a p-series with p = 2, and therefore converges, the original series

must also converge by the comparison test.

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