What is the sum from k=0 to infinity of (5x)^k ?

The sum from k=0 to infinity of (5x)^k is Interval of convergence is-1/5 <x< 1/5

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sum from k=0 to infinity of (5x)^k

k = 0 \sum \infty (5 x)^{k}

Interval of convergence is - \frac{1}{5} < x < \frac{1}{5}

Solution steps

k = 0 \sum \infty (5 x)^{k}

Use the Root Test to compute the convergence interval

Interval of convergence is - \frac{1}{5} < x < \frac{1}{5}

x \to \infty lim (4^{- x})

\frac{\partial}{\partial x} (\frac{1}{2 x})

\frac{d}{d t} (k t e^{3 t})

\frac{d}{d x} (\frac{2 x}{x - 1})

\frac{d ^{2}}{d x ^{2}} (\frac{3}{4 x ^{6}})

What is the sum from k=0 to infinity of (5x)^k ?
The sum from k=0 to infinity of (5x)^k is Interval of convergence is-1/5 <x< 1/5