What is the sum from k=4 to infinity of 1/(2k^2+k) ?

The sum from k=4 to infinity of 1/(2k^2+k) is converges

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sum from k=4 to infinity of 1/(2k^2+k)

k = 4 \sum \infty \frac{1}{2 k ^{2} + k}

converges

Solution steps

k = 4 \sum \infty \frac{1}{2 k ^{2} + k}

Apply Series Comparison Test:

converges

= converges

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

n = 1 \sum \infty \frac{2}{( n + 2 ) n}

n = 5 \sum \infty \frac{4 ^{n}}{5 ^{n}}

n = 1 \sum \infty \frac{n + 6}{n ^{2}}

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

What is the sum from k=4 to infinity of 1/(2k^2+k) ?
The sum from k=4 to infinity of 1/(2k^2+k) is converges