What is the sum from n=1 to infinity of 1/(5+n^2) ?

The sum from n=1 to infinity of 1/(5+n^2) is converges

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sum from n=1 to infinity of 1/(5+n^2)

n = 1 \sum \infty \frac{1}{5 + n ^{2}}

converges

Solution steps

n = 1 \sum \infty \frac{1}{5 + n ^{2}}

Apply Series Comparison Test:

converges

= converges

n = 2 \sum \infty \frac{3}{n ln ( n )}

n = 1 \sum \infty \frac{2}{( 4 n ^{2} - 1 )}

n = 1 \sum \infty (e)^{- n}

n = 2 \sum \infty \frac{1}{n} - \frac{1}{4 ^{n}}

n = 1 \sum \infty \frac{5 n}{5 n + 1}

What is the sum from n=1 to infinity of 1/(5+n^2) ?
The sum from n=1 to infinity of 1/(5+n^2) is converges