What is the sum from n=0 to infinity of-4(-1/6)^n ?

The sum from n=0 to infinity of-4(-1/6)^n is -24/7

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sum from n=0 to infinity of-4(-1/6)^n

n = 0 \sum \infty - 4 (- \frac{1}{6})^{n}

- \frac{24}{7}

Solution steps

n = 0 \sum \infty - 4 (- \frac{1}{6})^{n}

Apply the constant multiplication rule:

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

= - 4 \cdot n = 0 \sum \infty (- \frac{1}{6})^{n}

Apply Series Geometric Test:

\frac{6}{7}

= - 4 \cdot \frac{6}{7}

Simplify

- 4 \cdot \frac{6}{7} : - \frac{24}{7}

= - \frac{24}{7}

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What is the sum from n=0 to infinity of-4(-1/6)^n ?
The sum from n=0 to infinity of-4(-1/6)^n is -24/7