What is the sum from k=1 to infinity of (5k)/(e^{2k)} ?

The sum from k=1 to infinity of (5k)/(e^{2k)} is converges

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sum from k=1 to infinity of (5k)/(e^{2k)}

k = 1 \sum \infty \frac{5 k}{e ^{2 k}}

converges

Solution steps

k = 1 \sum \infty \frac{5 k}{e ^{2 k}}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 5 \cdot k = 1 \sum \infty \frac{k}{e ^{2 k}}

Apply Series Ratio Test:

converges

= 5 converges

= converges

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What is the sum from k=1 to infinity of (5k)/(e^{2k)} ?
The sum from k=1 to infinity of (5k)/(e^{2k)} is converges