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

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

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

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

\frac{6}{7}

Decimal

0.85714 \dots

Solution steps

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

Apply Series Geometric Test:

\frac{6}{7}

= \frac{6}{7}

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