What is the sum from n=0 to infinity of 5(3/pi)^n ?

The sum from n=0 to infinity of 5(3/pi)^n is 5*pi/(pi-3)

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sum from n=0 to infinity of 5(3/pi)^n

n = 0 \sum \infty 5 (\frac{3}{π})^{n}

5 \cdot \frac{π}{π - 3}

Solution steps

n = 0 \sum \infty 5 (\frac{3}{π})^{n}

Apply the constant multiplication rule:

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

= 5 \cdot n = 0 \sum \infty (\frac{3}{π})^{n}

Apply Series Geometric Test:

\frac{π}{π - 3}

= 5 \cdot \frac{π}{π - 3}

n = 1 \sum \infty (\frac{- 1}{7})^{n}

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

n = 0 \sum \infty (\frac{- 1}{4})^{n}

n = 2 \sum \infty \frac{1}{ln ( n ^{3} )}

n = 3 \sum \infty 5 (\frac{4}{9})^{n}

What is the sum from n=0 to infinity of 5(3/pi)^n ?
The sum from n=0 to infinity of 5(3/pi)^n is 5*pi/(pi-3)