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

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

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

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

Interval of convergence is 0 \leq p < 2

Solution steps

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

Use the Ratio Test to compute the convergence interval

Interval of convergence is 0 \leq p < 2

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