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

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

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

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

n = 1 \sum \infty 12 (- \frac{5}{8})^{n}

n = 2 \sum \infty 7 (- \frac{3}{8})^{n}

n = 2 \sum \infty (\frac{3}{5})^{4 n}

n = 0 \sum \infty 8 (\frac{1}{10})^{n}

n = 1 \sum \infty 4 n

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