What is the sum from n=0 to infinity of n/(2^n) ?

The sum from n=0 to infinity of n/(2^n) is converges

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sum from n=0 to infinity of n/(2^n)

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

9 e^{x} + x

x \to - 4 lim (\frac{x ^{2} - 2}{4 - x})

ln (5 x^{4})

\int \frac{x ^{2}}{4} d x

\frac{\partial}{\partial x} ((e^{2 y} - y cos (x y)) d x)

What is the sum from n=0 to infinity of n/(2^n) ?
The sum from n=0 to infinity of n/(2^n) is converges