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

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

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

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

1

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Geometric Test:

2

= \frac{1}{2} \cdot 2

Simplify

\frac{1}{2} \cdot 2 : 1

= 1

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