What is the sum from n=0 to infinity of p^n ?

The sum from n=0 to infinity of p^n is Radius of convergence is 1, Interval of convergence is-1<p<1

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sum from n=0 to infinity of p^n

n = 0 \sum \infty p^{n}

Radius of convergence is 1, Interval of convergence is - 1 < p < 1

Solution steps

n = 0 \sum \infty p^{n}

Use the Root Test to compute the convergence interval

Radius of convergence is 1, Interval of convergence is - 1 < p < 1

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