What is the sum from n=0 to infinity of (5/7)^n ?

The sum from n=0 to infinity of (5/7)^n is 7/2

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sum from n=0 to infinity of (5/7)^n

n = 0 \sum \infty (\frac{5}{7})^{n}

\frac{7}{2}

Solution steps

n = 0 \sum \infty (\frac{5}{7})^{n}

Apply Series Geometric Test:

\frac{7}{2}

= \frac{7}{2}

n = 1 \sum \infty \frac{n !}{9 ^{n}}

k = 1 \sum \infty \frac{4}{k} - \frac{4}{k + 1}

n = 1 \sum \infty \frac{1}{3 n ^{2} + 8}

k = 6 \sum \infty \frac{1}{k ^{2} - 5 k + 6}

n = 2 \sum \infty \frac{1}{4 n ^{3}}

What is the sum from n=0 to infinity of (5/7)^n ?
The sum from n=0 to infinity of (5/7)^n is 7/2