What is the sum from n=0 to infinity of 9(-0.8)^n ?

The sum from n=0 to infinity of 9(-0.8)^n is 5

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sum from n=0 to infinity of 9(-0.8)^n

n = 0 \sum \infty 9 (- 0.8)^{n}

5

Solution steps

n = 0 \sum \infty 9 (- 0.8)^{n}

Apply the constant multiplication rule:

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

= 9 \cdot n = 0 \sum \infty (- 0.8)^{n}

Apply Series Geometric Test:

0.55555 \dots

= 9 \cdot 0.55555 \dots

Simplify

= 5

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What is the sum from n=0 to infinity of 9(-0.8)^n ?
The sum from n=0 to infinity of 9(-0.8)^n is 5