What is the sum from n=0 to infinity of 2^{-n} ?

The sum from n=0 to infinity of 2^{-n} is 2

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sum from n=0 to infinity of 2^{-n}

n = 0 \sum \infty 2^{- n}

2

Solution steps

n = 0 \sum \infty 2^{- n}

Simplify

2^{- n} : \frac{1}{2 ^{n}}

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

Apply Series Geometric Test:

2

= 2

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What is the sum from n=0 to infinity of 2^{-n} ?
The sum from n=0 to infinity of 2^{-n} is 2