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

The sum from n=0 to infinity of 2/(2^n) is 4

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

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

4

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Geometric Test:

2

= 2 \cdot 2

Simplify

= 4

n = 0 \sum \infty ln (1 - n)

k = 0 \sum \infty \frac{k}{k + 1}

n = 1 \sum \infty 2^{n} - n

n = 0 \sum \infty \frac{n}{n + 5}

n = 1 \sum \infty \frac{8}{n}

What is the sum from n=0 to infinity of 2/(2^n) ?
The sum from n=0 to infinity of 2/(2^n) is 4