What is the sum from n=0 to infinity of 7(1/10)^n ?

The sum from n=0 to infinity of 7(1/10)^n is 70/9

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sum from n=0 to infinity of 7(1/10)^n

n = 0 \sum \infty 7 (\frac{1}{10})^{n}

\frac{70}{9}

Solution steps

n = 0 \sum \infty 7 (\frac{1}{10})^{n}

Apply the constant multiplication rule:

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

= 7 \cdot n = 0 \sum \infty (\frac{1}{10})^{n}

Apply Series Geometric Test:

\frac{10}{9}

= 7 \cdot \frac{10}{9}

Simplify

7 \cdot \frac{10}{9} : \frac{70}{9}

= \frac{70}{9}

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What is the sum from n=0 to infinity of 7(1/10)^n ?
The sum from n=0 to infinity of 7(1/10)^n is 70/9