What is the sum from k=0 to infinity of (-5/6)^k ?

The sum from k=0 to infinity of (-5/6)^k is 6/11

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sum from k=0 to infinity of (-5/6)^k

k = 0 \sum \infty (- \frac{5}{6})^{k}

\frac{6}{11}

Solution steps

k = 0 \sum \infty (- \frac{5}{6})^{k}

Apply Series Geometric Test:

\frac{6}{11}

= \frac{6}{11}

n = 1 \sum \infty (\frac{1}{100})^{n}

n = 0 \sum \infty \frac{n}{n ^{3}}

n = 6 \sum \infty ln (\frac{n}{3})

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

n = 1 \sum \infty 2 (\frac{1}{4})^{n - 1}

What is the sum from k=0 to infinity of (-5/6)^k ?
The sum from k=0 to infinity of (-5/6)^k is 6/11