What is the sum from k=0 to infinity of (0.5)^k ?

The sum from k=0 to infinity of (0.5)^k is 2

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sum from k=0 to infinity of (0.5)^k

k = 0 \sum \infty (0.5)^{k}

2

Solution steps

k = 0 \sum \infty 0. 5^{k}

Apply Series Geometric Test:

2

= 2

n = 1 \sum \infty \frac{π ^{n}}{3 ^{n}}

n = 1 \sum \infty (- 10)^{- n}

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

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

n = 1 \sum \infty 0. 9^{n}

What is the sum from k=0 to infinity of (0.5)^k ?
The sum from k=0 to infinity of (0.5)^k is 2