What is the sum from n=0 to infinity of 1/(2n^2+n) ?

The sum from n=0 to infinity of 1/(2n^2+n) is converges

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sum from n=0 to infinity of 1/(2n^2+n)

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

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

n = 3 \sum \infty n e^{- n^{2}}

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

n = 3 \sum \infty \frac{2}{3 ln ( n )}

What is the sum from n=0 to infinity of 1/(2n^2+n) ?
The sum from n=0 to infinity of 1/(2n^2+n) is converges