What is the sum from n=0 to infinity of 6(-2/3)^n ?

The sum from n=0 to infinity of 6(-2/3)^n is 18/5

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sum from n=0 to infinity of 6(-2/3)^n

n = 0 \sum \infty 6 (- \frac{2}{3})^{n}

\frac{18}{5}

Solution steps

n = 0 \sum \infty 6 (- \frac{2}{3})^{n}

Apply the constant multiplication rule:

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

= 6 \cdot n = 0 \sum \infty (- \frac{2}{3})^{n}

Apply Series Geometric Test:

\frac{3}{5}

= 6 \cdot \frac{3}{5}

Simplify

6 \cdot \frac{3}{5} : \frac{18}{5}

= \frac{18}{5}

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What is the sum from n=0 to infinity of 6(-2/3)^n ?
The sum from n=0 to infinity of 6(-2/3)^n is 18/5