What is the sum from n=1 to infinity of (-5x)^n ?

The sum from n=1 to infinity of (-5x)^n is Interval of convergence is-1/5 <x< 1/5

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sum from n=1 to infinity of (-5x)^n

n = 1 \sum \infty (- 5 x)^{n}

Interval of convergence is - \frac{1}{5} < x < \frac{1}{5}

Solution steps

n = 1 \sum \infty (- 5 x)^{n}

Use the Root Test to compute the convergence interval

Interval of convergence is - \frac{1}{5} < x < \frac{1}{5}

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What is the sum from n=1 to infinity of (-5x)^n ?
The sum from n=1 to infinity of (-5x)^n is Interval of convergence is-1/5 <x< 1/5