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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

k = 0 \sum \infty (\frac{5}{6})^{k}

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

n = 6 \sum \infty \frac{1}{( n - 3 ) ^{4}}

n = 1 \sum \infty \frac{1}{n ^{7} + 8}

n = 0 \sum \infty \frac{3}{- 3 ^{n}}

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