Example: The series converges.

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We will use the limit 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 comparision test.

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