What is the sum from n=0 to infinity of 1/(1+n^2) ?

The sum from n=0 to infinity of 1/(1+n^2) is converges

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sum from n=0 to infinity of 1/(1+n^2)

n = 0 \sum \infty \frac{1}{1 + n ^{2}}

converges

Solution steps

n = 0 \sum \infty \frac{1}{1 + n ^{2}}

Apply Series Comparison Test:

converges

= converges

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\frac{d}{d x} (- \frac{2}{5 x})

\frac{x ^{4}}{4} - \frac{3 x ^{2}}{4} + x - 2

What is the sum from n=0 to infinity of 1/(1+n^2) ?
The sum from n=0 to infinity of 1/(1+n^2) is converges