What is the sum from n=0 to infinity of 5/(2^n) ?

The sum from n=0 to infinity of 5/(2^n) is 10

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sum from n=0 to infinity of 5/(2^n)

n = 0 \sum \infty \frac{5}{2 ^{n}}

10

Solution steps

n = 0 \sum \infty \frac{5}{2 ^{n}}

Apply the constant multiplication rule:

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

= 5 \cdot n = 0 \sum \infty \frac{1}{2 ^{n}}

Apply Series Geometric Test:

2

= 5 \cdot 2

Simplify

= 10

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What is the sum from n=0 to infinity of 5/(2^n) ?
The sum from n=0 to infinity of 5/(2^n) is 10