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

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

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

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

n = 0 \sum \infty ln (9 - n)

n = 1 \sum \infty 1 + n

n = 0 \sum \infty (\frac{1}{3})^{3 n}

n = 1 \sum \infty \frac{4 n}{5 ^{n} + 2}

n = 1 \sum \infty n 14

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