What is the sum from n=0 to infinity of (3x)^n ?

The sum from n=0 to infinity of (3x)^n is Interval of convergence is-1/3 <x< 1/3

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sum from n=0 to infinity of (3x)^n

n = 0 \sum \infty (3 x)^{n}

Interval of convergence is - \frac{1}{3} < x < \frac{1}{3}

Solution steps

n = 0 \sum \infty (3 x)^{n}

Use the Root Test to compute the convergence interval

Interval of convergence is - \frac{1}{3} < x < \frac{1}{3}

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What is the sum from n=0 to infinity of (3x)^n ?
The sum from n=0 to infinity of (3x)^n is Interval of convergence is-1/3 <x< 1/3