What is the sum from k=0 to infinity of (-2/9)^k ?

The sum from k=0 to infinity of (-2/9)^k is 9/11

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sum from k=0 to infinity of (-2/9)^k

k = 0 \sum \infty (- \frac{2}{9})^{k}

\frac{9}{11}

Solution steps

k = 0 \sum \infty (- \frac{2}{9})^{k}

Apply Series Geometric Test:

\frac{9}{11}

= \frac{9}{11}

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What is the sum from k=0 to infinity of (-2/9)^k ?
The sum from k=0 to infinity of (-2/9)^k is 9/11