What is the sum from n=0 to infinity of (2^n)/(8^n) ?

The sum from n=0 to infinity of (2^n)/(8^n) is 4/3

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sum from n=0 to infinity of (2^n)/(8^n)

n = 0 \sum \infty \frac{2 ^{n}}{8 ^{n}}

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

n = 0 \sum \infty \frac{2 ^{n}}{8 ^{n}}

Simplify

\frac{2 ^{n}}{8 ^{n}} : (\frac{1}{4})^{n}

= n = 0 \sum \infty (\frac{1}{4})^{n}

Apply Series Geometric Test:

\frac{4}{3}

= \frac{4}{3}

What is the sum from n=0 to infinity of (2^n)/(8^n) ?
The sum from n=0 to infinity of (2^n)/(8^n) is 4/3