What is the sum from n=0 to infinity of 9/(pi^n) ?

The sum from n=0 to infinity of 9/(pi^n) is 9*pi/(pi-1)

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sum from n=0 to infinity of 9/(pi^n)

n = 0 \sum \infty \frac{9}{π ^{n}}

9 \cdot \frac{π}{π - 1}

Decimal

13.20247 \dots

Solution steps

n = 0 \sum \infty \frac{9}{π ^{n}}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 9 \cdot n = 0 \sum \infty \frac{1}{π ^{n}}

Apply Series Geometric Test:

\frac{π}{π - 1}

= 9 \cdot \frac{π}{π - 1}

What is the sum from n=0 to infinity of 9/(pi^n) ?
The sum from n=0 to infinity of 9/(pi^n) is 9*pi/(pi-1)