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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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