What is the sum from n=0 to infinity of 9/2 (1/2)^n ?

The sum from n=0 to infinity of 9/2 (1/2)^n is 9

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sum from n=0 to infinity of 9/2 (1/2)^n

n = 0 \sum \infty \frac{9}{2} (\frac{1}{2})^{n}

9

Solution steps

n = 0 \sum \infty \frac{9}{2} (\frac{1}{2})^{n}

Apply the constant multiplication rule:

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

= \frac{9}{2} \cdot n = 0 \sum \infty (\frac{1}{2})^{n}

Apply Series Geometric Test:

2

= \frac{9}{2} \cdot 2

Simplify

\frac{9}{2} \cdot 2 : 9

= 9

n = 0 \sum \infty \frac{n ^{2} + 1}{n}

k = 0 \sum \infty (\frac{1}{2})^{k}

n = 0 \sum \infty \frac{10 n}{4 n + 1}

n = 1 \sum \infty \frac{9}{5 n ^{3}}

n = 0 \sum \infty \frac{n}{1}

What is the sum from n=0 to infinity of 9/2 (1/2)^n ?
The sum from n=0 to infinity of 9/2 (1/2)^n is 9