What is the sum from n=0 to infinity of pi^{-n} ?

The sum from n=0 to infinity of pi^{-n} is pi/(pi-1)

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sum from n=0 to infinity of pi^{-n}

n = 0 \sum \infty π^{- n}

\frac{π}{π - 1}

Solution steps

n = 0 \sum \infty π^{- n}

Simplify

π^{- n} : \frac{1}{π ^{n}}

= n = 0 \sum \infty \frac{1}{π ^{n}}

Apply Series Geometric Test:

\frac{π}{π - 1}

= \frac{π}{π - 1}

n = 1 \sum \infty \frac{n}{5 n ^{2} + 3}

n = 0 \sum \infty \frac{2}{n}

n = 1 \sum \infty \frac{n}{sin ( n )}

n = 1 \sum \infty 2 + e^{- n}

n = 0 \sum \infty \frac{- 1 ^{n}}{2 ^{n}}

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