What is the sum from n=0 to infinity of 7/(pi^n) ?

The sum from n=0 to infinity of 7/(pi^n) is 7*pi/(pi-1)

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sum from n=0 to infinity of 7/(pi^n)

n = 0 \sum \infty \frac{7}{π ^{n}}

7 \cdot \frac{π}{π - 1}

Solution steps

n = 0 \sum \infty \frac{7}{π ^{n}}

Apply the constant multiplication rule:

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

= 7 \cdot n = 0 \sum \infty \frac{1}{π ^{n}}

Apply Series Geometric Test:

\frac{π}{π - 1}

= 7 \cdot \frac{π}{π - 1}

n = 1 \sum \infty sin (3 n)

n = 0 \sum \infty \frac{2}{( - 3 ) ^{n}}

n = 1 \sum \infty \frac{2}{3 n - 1}

n = 2 \sum \infty \frac{- 1}{ln ( n )}

n = 3 \sum \infty \frac{7}{n} - \frac{7}{n + 2}

What is the sum from n=0 to infinity of 7/(pi^n) ?
The sum from n=0 to infinity of 7/(pi^n) is 7*pi/(pi-1)