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

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

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sum from k=1 to infinity of k/(2^{k-1)}

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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

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

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

n = 1 \sum \infty \frac{2}{n} - \frac{2}{n + 1}

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

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