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

The sum from k=0 to infinity of k/(2k+1) is diverges

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

k = 0 \sum \infty \frac{k}{2 k + 1}

diverges

Solution steps

k = 0 \sum \infty \frac{k}{2 k + 1}

Apply Series Divergence Test:

diverges

= diverges

n = 0 \sum \infty \frac{1}{n ^{2} - 2 n}

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

n = 1 \sum \infty e^{- \frac{n}{6}}

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

n = 4 \sum \infty \frac{2}{5 n ^{3}}

What is the sum from k=0 to infinity of k/(2k+1) ?
The sum from k=0 to infinity of k/(2k+1) is diverges