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

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

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

k = 0 \sum \infty (\frac{2}{5})^{k}

\frac{5}{3}

Solution steps

k = 0 \sum \infty (\frac{2}{5})^{k}

Apply Series Geometric Test:

\frac{5}{3}

= \frac{5}{3}

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

n = 0 \sum \infty 2^{n} + i

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

n = 1 \sum \infty \frac{3}{9 ^{n + 1}}

n = 1 \sum \infty 2 n + 3

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