What is the sum from n=0 to infinity of p(1-p)^n ?

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

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sum from n=0 to infinity of p(1-p)^n

n = 0 \sum \infty p (1 - p)^{n}

Interval of convergence is 0 \leq p < 2

Solution steps

n = 0 \sum \infty p (1 - p)^{n}

Use the Ratio Test to compute the convergence interval

Interval of convergence is 0 \leq p < 2

e^{- x^{2}} cos (x)

\int e^{2 x} \cdot sin (3 x) d x

\frac{d}{d x} (csc^{4} (x))

\frac{d}{d x} (\frac{e ^{2 x}}{x})

n = 0 \sum \infty \frac{5}{n !}

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