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

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

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

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

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

Solution steps

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

Use the Root Test to compute the convergence interval

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

f (x) = x 2^{x}

(- 2.3) (2.2)

x \to 0 - lim (x \cdot arctan (\frac{1}{x}))

\frac{d y}{d x} = \frac{2 x}{1 + 2 y}, y (2) = 0

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

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