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

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

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

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

\int \frac{1}{( 4 + x ^{2} )} d x

y = \frac{2}{3} (x^{2} + 1)^{\frac{3}{2}}

y = 5 x tan (x), at x = π

f (x) = 3^{x^{5}}

x \to 0 + lim (x^{(\frac{1}{x})})

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