What is the sum from k=1 to infinity of k/(e^{6k)} ?

The sum from k=1 to infinity of k/(e^{6k)} is converges

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sum from k=1 to infinity of k/(e^{6k)}

k = 1 \sum \infty \frac{k}{e ^{6 k}}

converges

Solution steps

k = 1 \sum \infty \frac{k}{e ^{6 k}}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{n}{10 n - 3}

n = 0 \sum \infty 5 (\frac{5}{2})^{n}

n = 1 \sum \infty cos (\frac{4}{n})

n = 0 \sum \infty (\frac{1}{100})^{n}

n = 0 \sum \infty \frac{9}{2 ^{n}}

What is the sum from k=1 to infinity of k/(e^{6k)} ?
The sum from k=1 to infinity of k/(e^{6k)} is converges