What is the sum from n=1 to infinity of 2^nx^{n-1} ?

The sum from n=1 to infinity of 2^nx^{n-1} is Radius of convergence is 1/2

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sum from n=1 to infinity of 2^nx^{n-1}

n = 1 \sum \infty 2^{n} x^{n - 1}

Radius of convergence is \frac{1}{2}

Solution steps

n = 1 \sum \infty 2^{n} x^{n - 1}

Use the Ratio Test to compute the convergence interval

Radius of convergence is \frac{1}{2}

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What is the sum from n=1 to infinity of 2^nx^{n-1} ?
The sum from n=1 to infinity of 2^nx^{n-1} is Radius of convergence is 1/2