What is the sum from n=0 to infinity of (n+1)(1/2)^n ?

The sum from n=0 to infinity of (n+1)(1/2)^n is converges

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sum from n=0 to infinity of (n+1)(1/2)^n

n = 0 \sum \infty (n + 1) (\frac{1}{2})^{n}

converges

Solution steps

n = 0 \sum \infty (n + 1) (\frac{1}{2})^{n}

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=0 to infinity of (n+1)(1/2)^n ?
The sum from n=0 to infinity of (n+1)(1/2)^n is converges