What is the sum from n=1 to infinity of (3/pi)^n ?

The sum from n=1 to infinity of (3/pi)^n is converges

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sum from n=1 to infinity of (3/pi)^n

n = 1 \sum \infty (\frac{3}{π})^{n}

converges

Solution steps

n = 1 \sum \infty (\frac{3}{π})^{n}

Apply Series Ratio Test:

converges

= converges

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

n = 1 \sum \infty \frac{1}{3 + 4 ^{- n}}

k = 1 \sum \infty 5 (- \frac{1}{6})^{5 k}

n = 1 \sum \infty \frac{3}{n ^{3} + 7}

n = 1 \sum \infty (\frac{4}{7})^{n - 1}

What is the sum from n=1 to infinity of (3/pi)^n ?
The sum from n=1 to infinity of (3/pi)^n is converges