What is the sum from n=0 to infinity of 2^nn^2x^n ?

The sum from n=0 to infinity of 2^nn^2x^n is Radius of convergence is 1/2

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sum from n=0 to infinity of 2^nn^2x^n

n = 0 \sum \infty 2^{n} n^{2} x^{n}

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

Solution steps

n = 0 \sum \infty 2^{n} n^{2} x^{n}

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=0 to infinity of 2^nn^2x^n ?
The sum from n=0 to infinity of 2^nn^2x^n is Radius of convergence is 1/2