What is the sum from k=0 to infinity of (-5/8)^k ?

The sum from k=0 to infinity of (-5/8)^k is 8/13

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sum from k=0 to infinity of (-5/8)^k

k = 0 \sum \infty (- \frac{5}{8})^{k}

\frac{8}{13}

Solution steps

k = 0 \sum \infty (- \frac{5}{8})^{k}

Apply Series Geometric Test:

\frac{8}{13}

= \frac{8}{13}

n = 1 \sum \infty \frac{1 - n}{n ^{2}}

n = 0 \sum \infty - ln (3 - n)

n = 1 \sum \infty (0.6)^{n}

k = 0 \sum \infty \frac{k}{8 k + 1}

n = 2 \sum \infty [\frac{2}{5 ^{n}}]

What is the sum from k=0 to infinity of (-5/8)^k ?
The sum from k=0 to infinity of (-5/8)^k is 8/13