What is the sum from n=0 to infinity of 3/2 (1/2)^n ?

The sum from n=0 to infinity of 3/2 (1/2)^n is 3

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sum from n=0 to infinity of 3/2 (1/2)^n

n = 0 \sum \infty \frac{3}{2} (\frac{1}{2})^{n}

3

Solution steps

n = 0 \sum \infty \frac{3}{2} (\frac{1}{2})^{n}

Apply the constant multiplication rule:

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

= \frac{3}{2} \cdot n = 0 \sum \infty (\frac{1}{2})^{n}

Apply Series Geometric Test:

2

= \frac{3}{2} \cdot 2

Simplify

\frac{3}{2} \cdot 2 : 3

= 3

n = 1 \sum \infty \frac{3}{( 4 n + 2 ) ^{3}}

k = 0 \sum \infty 2^{k}

n = 1 \sum \infty \frac{ln ( 5 n )}{n}

k = 2 \sum \infty \frac{1}{k ^{2} - k}

k = 1 \sum \infty \frac{1}{2 ^{k} + k}

What is the sum from n=0 to infinity of 3/2 (1/2)^n ?
The sum from n=0 to infinity of 3/2 (1/2)^n is 3