What is the sum from n=0 to infinity of 4/(3^n) ?

The sum from n=0 to infinity of 4/(3^n) is 6

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sum from n=0 to infinity of 4/(3^n)

n = 0 \sum \infty \frac{4}{3 ^{n}}

6

Solution steps

n = 0 \sum \infty \frac{4}{3 ^{n}}

Apply the constant multiplication rule:

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

= 4 \cdot n = 0 \sum \infty \frac{1}{3 ^{n}}

Apply Series Geometric Test:

\frac{3}{2}

= 4 \cdot \frac{3}{2}

Simplify

4 \cdot \frac{3}{2} : 6

= 6

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What is the sum from n=0 to infinity of 4/(3^n) ?
The sum from n=0 to infinity of 4/(3^n) is 6