What is the sum from n=1 to infinity of 1/(25n^2-1) ?

The sum from n=1 to infinity of 1/(25n^2-1) is converges

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sum from n=1 to infinity of 1/(25n^2-1)

n = 1 \sum \infty \frac{1}{25 n ^{2} - 1}

converges

Solution steps

n = 1 \sum \infty \frac{1}{25 n ^{2} - 1}

Apply Series Integral Test:

converges

= converges

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

n = 1 \sum \infty \frac{sin ( 1 )}{n}

n = 1 \sum \infty \frac{n}{6 n ^{3} + 5}

n = 0 \sum \infty 5 n^{2}

n = 2 \sum \infty \frac{1}{3 n + 4}

What is the sum from n=1 to infinity of 1/(25n^2-1) ?
The sum from n=1 to infinity of 1/(25n^2-1) is converges