What is the sum from k=0 to infinity of (1/2)^k ?

The sum from k=0 to infinity of (1/2)^k is 2

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sum from k=0 to infinity of (1/2)^k

k = 0 \sum \infty (\frac{1}{2})^{k}

2

Solution steps

k = 0 \sum \infty (\frac{1}{2})^{k}

Apply Series Geometric Test:

2

= 2

n = 0 \sum \infty \frac{10 n}{4 n + 1}

n = 1 \sum \infty \frac{9}{5 n ^{3}}

n = 0 \sum \infty \frac{n}{1}

n = 0 \sum \infty \frac{4}{n}

n = 1 \sum \infty \frac{2}{n ^{0.45}}

What is the sum from k=0 to infinity of (1/2)^k ?
The sum from k=0 to infinity of (1/2)^k is 2