What is the sum from k=1 to infinity of k(2/3)^k ?

The sum from k=1 to infinity of k(2/3)^k is converges

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sum from k=1 to infinity of k(2/3)^k

k = 1 \sum \infty k (\frac{2}{3})^{k}

converges

Solution steps

k = 1 \sum \infty k (\frac{2}{3})^{k}

Apply Series Ratio Test:

converges

= converges

sin (t - 1)

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\int \frac{4}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

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What is the sum from k=1 to infinity of k(2/3)^k ?
The sum from k=1 to infinity of k(2/3)^k is converges