What is the sum from n=1 to infinity of (2^nx^n)/n ?

The sum from n=1 to infinity of (2^nx^n)/n is Radius of convergence is 1/2

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sum from n=1 to infinity of (2^nx^n)/n

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

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

Solution steps

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

Use the Ratio Test to compute the convergence interval

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

\int \frac{x ^{2}}{1 + x ^{2}} d x

\frac{d}{d x} (e^{x} + 3)

\int_{1}^{9} u + 2 d u

\int \frac{x ^{4} + 3 x ^{2} + 1}{x ^{5} + 5 x ^{3} + 5 x} d x

\int e^{\frac{- x}{2}} d x

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