What is the sum from n=0 to infinity of 5(-10/11)^n ?

The sum from n=0 to infinity of 5(-10/11)^n is 55/21

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sum from n=0 to infinity of 5(-10/11)^n

n = 0 \sum \infty 5 (- \frac{10}{11})^{n}

\frac{55}{21}

Decimal

2.61904 \dots

Solution steps

n = 0 \sum \infty 5 (- \frac{10}{11})^{n}

Apply the constant multiplication rule:

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

= 5 \cdot n = 0 \sum \infty (- \frac{10}{11})^{n}

Apply Series Geometric Test:

\frac{11}{21}

= 5 \cdot \frac{11}{21}

Simplify

5 \cdot \frac{11}{21} : \frac{55}{21}

= \frac{55}{21}

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What is the sum from n=0 to infinity of 5(-10/11)^n ?
The sum from n=0 to infinity of 5(-10/11)^n is 55/21