What is the sum from n=0 to infinity of 5/(4^n) ?

The sum from n=0 to infinity of 5/(4^n) is 20/3

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sum from n=0 to infinity of 5/(4^n)

n = 0 \sum \infty \frac{5}{4 ^{n}}

\frac{20}{3}

Decimal

6.66666 \dots

Solution steps

n = 0 \sum \infty \frac{5}{4 ^{n}}

Apply the constant multiplication rule:

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

= 5 \cdot n = 0 \sum \infty \frac{1}{4 ^{n}}

Apply Series Geometric Test:

\frac{4}{3}

= 5 \cdot \frac{4}{3}

Simplify

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

= \frac{20}{3}

What is the sum from n=0 to infinity of 5/(4^n) ?
The sum from n=0 to infinity of 5/(4^n) is 20/3