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

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

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

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

5

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Geometric Test:

\frac{5}{4}

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

Simplify

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

= 5

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