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

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

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

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

converges

Solution steps

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

Apply Series Integral Test:

converges

= converges

\int (x + 4) d x

\int \frac{9}{x ( x ^{4} + 5 )} d x

f (t) = 2 cos (t) + sin (2 t)

f (x) = x^{2} - 1

- 3 x^{4} - \frac{1}{x} + x x

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