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

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

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

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

n = 1 \sum \infty (cos (6))^{n}

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

n = 0 \sum \infty 6^{- n}

n = 0 \sum \infty \frac{1}{( n + 1 ) ^{3}}

n = 1 \sum \infty (\frac{8}{7})^{n}

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