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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

x = 0 \sum \infty \frac{1}{x !}

n = 4 \sum \infty \frac{2}{n ( n - 1 )}

n = 1 \sum \infty \frac{n}{n ^{2} + 7}

n = 0 \sum \infty \frac{1}{n \cdot 3 ^{n}}

n = 0 \sum \infty 7

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