What is the sum from k=1 to infinity of k*2^{-k} ?

The sum from k=1 to infinity of k*2^{-k} is converges

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sum from k=1 to infinity of k*2^{-k}

k = 1 \sum \infty k \cdot 2^{- k}

converges

Solution steps

k = 1 \sum \infty k \cdot 2^{- k}

Apply Series Ratio Test:

converges

= converges

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What is the sum from k=1 to infinity of k*2^{-k} ?
The sum from k=1 to infinity of k*2^{-k} is converges