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

The sum from k=0 to infinity of (3/5)^k is 5/2

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

k = 0 \sum \infty (\frac{3}{5})^{k}

\frac{5}{2}

Solution steps

k = 0 \sum \infty (\frac{3}{5})^{k}

Apply Series Geometric Test:

\frac{5}{2}

= \frac{5}{2}

n = 1 \sum \infty 5 (\frac{1}{π})^{n}

n = 1 \sum \infty \frac{6}{n + 5}

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

n = 0 \sum \infty \frac{π}{2}

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

What is the sum from k=0 to infinity of (3/5)^k ?
The sum from k=0 to infinity of (3/5)^k is 5/2