What is the sum from n=1 to infinity of n/(2^n) ?

The sum from n=1 to infinity of n/(2^n) is converges

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sum from n=1 to infinity of n/(2^n)

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

(6, - 1), (- 3, - 10)

\frac{d}{d y} (\frac{y ^{3}}{30} + \frac{5}{2 y})

(x^{2} + 1)^{3}

y = \frac{2}{x - 8}

x \to 1 lim (\frac{1}{1 - x ^{2}})

What is the sum from n=1 to infinity of n/(2^n) ?
The sum from n=1 to infinity of n/(2^n) is converges