What is the sum from n=0 to infinity of (20)/(4^n) ?

The sum from n=0 to infinity of (20)/(4^n) is 80/3

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sum from n=0 to infinity of (20)/(4^n)

n = 0 \sum \infty \frac{20}{4 ^{n}}

\frac{80}{3}

Solution steps

n = 0 \sum \infty \frac{20}{4 ^{n}}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 20 \cdot n = 0 \sum \infty \frac{1}{4 ^{n}}

Apply Series Geometric Test:

\frac{4}{3}

= 20 \cdot \frac{4}{3}

Simplify

20 \cdot \frac{4}{3} : \frac{80}{3}

= \frac{80}{3}

n = 1 \sum \infty (\frac{π}{3})^{n}

k = 1 \sum \infty \frac{1}{k + 1}

n = 0 \sum \infty \frac{n}{9 + n ^{2}}

n = 0 \sum \infty 7 (\frac{2}{3})^{n + 2}

n = 1 \sum \infty \frac{e ^{\frac{8}{n}}}{n}

What is the sum from n=0 to infinity of (20)/(4^n) ?
The sum from n=0 to infinity of (20)/(4^n) is 80/3