What is the sum from k=2 to infinity of k/(k^3-k+1) ?

The sum from k=2 to infinity of k/(k^3-k+1) is converges

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sum from k=2 to infinity of k/(k^3-k+1)

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

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

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

n = 0 \sum \infty \frac{n !}{2 n ! + 1}

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

n = 1 \sum \infty (n)^{2}

What is the sum from k=2 to infinity of k/(k^3-k+1) ?
The sum from k=2 to infinity of k/(k^3-k+1) is converges