What is the sum from k=0 to infinity of (0.8)^k ?

The sum from k=0 to infinity of (0.8)^k is 5

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sum from k=0 to infinity of (0.8)^k

k = 0 \sum \infty (0.8)^{k}

5

Solution steps

k = 0 \sum \infty 0. 8^{k}

Apply Series Geometric Test:

5

= 5

n = 1 \sum \infty \frac{5}{1 + n ^{2}}

x = 0 \sum \infty \frac{1}{1 - x}

n = 1 \sum \infty 4^{n - 1}

n = 1 \sum \infty 2 (0.1)^{n - 1}

n = 1 \sum \infty \frac{3}{( 2 n + 5 ) ^{3}}

What is the sum from k=0 to infinity of (0.8)^k ?
The sum from k=0 to infinity of (0.8)^k is 5