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 8/3

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

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

\frac{8}{3}

Solution steps

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

Apply Series Geometric Test:

\frac{8}{3}

= \frac{8}{3}

n = 5 \sum \infty cos (\frac{1}{n + 1})

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

n = 1 \sum \infty (\frac{4}{25})^{n}

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

n = 1 \sum \infty \frac{n + 3}{8 ^{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 8/3