What is the sum from n=1 to infinity of (2^n)/n (4x-8)^n ?

The sum from n=1 to infinity of (2^n)/n (4x-8)^n is Radius of convergence is 1/8

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sum from n=1 to infinity of (2^n)/n (4x-8)^n

n = 1 \sum \infty \frac{2 ^{n}}{n} (4 x - 8)^{n}

Radius of convergence is \frac{1}{8}

Solution steps

n = 1 \sum \infty \frac{2 ^{n}}{n} (4 x - 8)^{n}

Use the Ratio Test to compute the convergence interval

Radius of convergence is \frac{1}{8}

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n = 1 \sum \infty 1^{n}

What is the sum from n=1 to infinity of (2^n)/n (4x-8)^n ?
The sum from n=1 to infinity of (2^n)/n (4x-8)^n is Radius of convergence is 1/8