What is the sum from k=0 to infinity of (1/4)^k ?

The sum from k=0 to infinity of (1/4)^k is 4/3

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sum from k=0 to infinity of (1/4)^k

k = 0 \sum \infty (\frac{1}{4})^{k}

\frac{4}{3}

Solution steps

k = 0 \sum \infty (\frac{1}{4})^{k}

Apply Series Geometric Test:

\frac{4}{3}

= \frac{4}{3}

n = 0 \sum \infty \frac{5}{n}

n = 1 \sum \infty \frac{8}{5 n + 12}

n = 0 \sum \infty \frac{2}{9 ^{n}}

n = 1 \sum \infty \frac{n}{3 n - 1}

n = 0 \sum \infty (- \frac{1}{8})^{n}

What is the sum from k=0 to infinity of (1/4)^k ?
The sum from k=0 to infinity of (1/4)^k is 4/3