What is the sum from n=0 to infinity of (5/12)^n ?

The sum from n=0 to infinity of (5/12)^n is 12/7

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sum from n=0 to infinity of (5/12)^n

n = 0 \sum \infty (\frac{5}{12})^{n}

\frac{12}{7}

Solution steps

n = 0 \sum \infty (\frac{5}{12})^{n}

Apply Series Geometric Test:

\frac{12}{7}

= \frac{12}{7}

n = 0 \sum \infty \frac{3}{5 ^{n}} + \frac{2}{n}

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

k = 0 \sum \infty (- \frac{2}{3})^{k}

n = 0 \sum \infty \frac{3}{5 ^{n + 2}}

n = 1 \sum \infty \frac{e}{π ^{n}}

What is the sum from n=0 to infinity of (5/12)^n ?
The sum from n=0 to infinity of (5/12)^n is 12/7