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

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

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

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

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

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

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

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

n = 1 \sum \infty \frac{8}{( - 3 ) ^{n}}

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