What is the sum from n=0 to infinity of 3(1/5)^n ?

The sum from n=0 to infinity of 3(1/5)^n is 15/4

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sum from n=0 to infinity of 3(1/5)^n

n = 0 \sum \infty 3 (\frac{1}{5})^{n}

\frac{15}{4}

Decimal

3.75

Solution steps

n = 0 \sum \infty 3 (\frac{1}{5})^{n}

Apply the constant multiplication rule:

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

= 3 \cdot n = 0 \sum \infty (\frac{1}{5})^{n}

Apply Series Geometric Test:

\frac{5}{4}

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

Simplify

3 \cdot \frac{5}{4} : \frac{15}{4}

= \frac{15}{4}

What is the sum from n=0 to infinity of 3(1/5)^n ?
The sum from n=0 to infinity of 3(1/5)^n is 15/4