What is the sum from n=0 to infinity of-6*(6/7)^n ?

The sum from n=0 to infinity of-6*(6/7)^n is -42

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sum from n=0 to infinity of-6*(6/7)^n

n = 0 \sum \infty - 6 \cdot (\frac{6}{7})^{n}

- 42

Solution steps

n = 0 \sum \infty - 6 (\frac{6}{7})^{n}

Apply the constant multiplication rule:

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

= - 6 \cdot n = 0 \sum \infty (\frac{6}{7})^{n}

Apply Series Geometric Test:

7

= - 6 \cdot 7

Simplify

= - 42

What is the sum from n=0 to infinity of-6*(6/7)^n ?
The sum from n=0 to infinity of-6*(6/7)^n is -42