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

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

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

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

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

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