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

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

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

i = 0 \sum \infty \frac{1}{2 ^{i}}

2

Solution steps

i = 0 \sum \infty \frac{1}{2 ^{i}}

Apply Series Geometric Test:

2

= 2

n = 3 \sum \infty \frac{4}{7 ^{n}}

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

n = 70 \sum \infty \frac{3}{n ^{2} + 2 n}

k = 1 \sum \infty (- \frac{1}{3})^{k}

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

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