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

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

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

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

n = 0 \sum \infty 1 - \frac{1}{n}

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

n = 0 \sum \infty \frac{1}{n ^{2} - 1}

k = 1 \sum \infty k e^{- k}

n = 1 \sum \infty \frac{n !}{n \cdot 2 ^{n}}

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