What is the sum from n=0 to infinity of (-2/3 x)^n ?

The sum from n=0 to infinity of (-2/3 x)^n is Interval of convergence is-3/2 <x< 3/2

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sum from n=0 to infinity of (-2/3 x)^n

n = 0 \sum \infty (- \frac{2}{3} x)^{n}

Interval of convergence is - \frac{3}{2} < x < \frac{3}{2}

Solution steps

n = 0 \sum \infty (- \frac{2}{3} x)^{n}

Use the Root Test to compute the convergence interval

Interval of convergence is - \frac{3}{2} < x < \frac{3}{2}

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{3 x ^{\frac{2}{3}}})

\frac{\partial}{\partial x} (- 3 x e^{x y})

(\frac{2 sin ( x )}{1 - 2 cos ( x )})^{^{'}}

x \to 0 - lim (\frac{9}{x} - \frac{9}{∣ x ∣})

x^{2} (x^{3} + 4) (x^{5} - 6)

What is the sum from n=0 to infinity of (-2/3 x)^n ?
The sum from n=0 to infinity of (-2/3 x)^n is Interval of convergence is-3/2 <x< 3/2