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

The sum from n=0 to infinity of x(2x)^n is Interval of convergence is-1/2 <x< 1/2

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sum from n=0 to infinity of x(2x)^n

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

Interval of convergence is - \frac{1}{2} < x < \frac{1}{2}

Solution steps

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

Use the Ratio Test to compute the convergence interval

Interval of convergence is - \frac{1}{2} < x < \frac{1}{2}

f (x) = x x, at x = 1

y^{^{''}} + \frac{1}{x} y^{^{'}} - \frac{1}{x ^{2}} y = \frac{2}{x}

y = \frac{e ^{x} + e ^{- x}}{2}

f (x) = e^{1 - x}

\int x^{2} arctan (7 x) d x

What is the sum from n=0 to infinity of x(2x)^n ?
The sum from n=0 to infinity of x(2x)^n is Interval of convergence is-1/2 <x< 1/2