What is the sum from n=0 to infinity of (-5/9)^n ?

The sum from n=0 to infinity of (-5/9)^n is 9/14

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sum from n=0 to infinity of (-5/9)^n

n = 0 \sum \infty (- \frac{5}{9})^{n}

\frac{9}{14}

Solution steps

n = 0 \sum \infty (- \frac{5}{9})^{n}

Apply Series Geometric Test:

\frac{9}{14}

= \frac{9}{14}

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What is the sum from n=0 to infinity of (-5/9)^n ?
The sum from n=0 to infinity of (-5/9)^n is 9/14