What is the sum from k=1 to infinity of k/(7^k) ?

The sum from k=1 to infinity of k/(7^k) is converges

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sum from k=1 to infinity of k/(7^k)

k = 1 \sum \infty \frac{k}{7 ^{k}}

converges

Solution steps

k = 1 \sum \infty \frac{k}{7 ^{k}}

Apply Series Ratio Test:

converges

= converges

\frac{d}{d x} (x (arcsin (x))^{2})

8 e^{x}

x \to \infty lim (2 x^{3} - 1)

\frac{d y}{d x} = \frac{( 1 + x y )}{1 + x}

\frac{x}{x + 9}

What is the sum from k=1 to infinity of k/(7^k) ?
The sum from k=1 to infinity of k/(7^k) is converges