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

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

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

k = 1 \sum \infty \frac{k}{e ^{k}}

converges

Solution steps

k = 1 \sum \infty \frac{k}{e ^{k}}

Apply Series Ratio Test:

converges

= converges

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

n = 1 \sum \infty \frac{1}{5 ^{n} + 1}

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

n = 1 \sum \infty \frac{5}{n ^{2} + 6}

n = 100 \sum \infty \frac{1}{n}

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