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

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

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

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

Interval of convergence is 0 < p < 2

Solution steps

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

Use the Ratio Test to compute the convergence interval

Interval of convergence is 0 < p < 2

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