What is the sum from n=0 to infinity of 9/4 (1/4)^n ?

The sum from n=0 to infinity of 9/4 (1/4)^n is 3

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sum from n=0 to infinity of 9/4 (1/4)^n

n = 0 \sum \infty \frac{9}{4} (\frac{1}{4})^{n}

3

Solution steps

n = 0 \sum \infty \frac{9}{4} (\frac{1}{4})^{n}

Apply the constant multiplication rule:

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

= \frac{9}{4} \cdot n = 0 \sum \infty (\frac{1}{4})^{n}

Apply Series Geometric Test:

\frac{4}{3}

= \frac{9}{4} \cdot \frac{4}{3}

Simplify

\frac{9}{4} \cdot \frac{4}{3} : 3

= 3

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What is the sum from n=0 to infinity of 9/4 (1/4)^n ?
The sum from n=0 to infinity of 9/4 (1/4)^n is 3