What is the sum from n=0 to infinity of (2^n)/(4^n) ?

The sum from n=0 to infinity of (2^n)/(4^n) is 2

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sum from n=0 to infinity of (2^n)/(4^n)

n = 0 \sum \infty \frac{2 ^{n}}{4 ^{n}}

2

Solution steps

n = 0 \sum \infty \frac{2 ^{n}}{4 ^{n}}

Simplify

\frac{2 ^{n}}{4 ^{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)/(4^n) ?
The sum from n=0 to infinity of (2^n)/(4^n) is 2