What is the sum from n=0 to infinity of 8(1/10)^n ?

The sum from n=0 to infinity of 8(1/10)^n is 80/9

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sum from n=0 to infinity of 8(1/10)^n

n = 0 \sum \infty 8 (\frac{1}{10})^{n}

\frac{80}{9}

Solution steps

n = 0 \sum \infty 8 (\frac{1}{10})^{n}

Apply the constant multiplication rule:

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

= 8 \cdot n = 0 \sum \infty (\frac{1}{10})^{n}

Apply Series Geometric Test:

\frac{10}{9}

= 8 \cdot \frac{10}{9}

Simplify

8 \cdot \frac{10}{9} : \frac{80}{9}

= \frac{80}{9}

n = 1 \sum \infty 4 n

n = 2 \sum \infty \frac{1}{n} - \frac{1}{n + 3}

n = 0 \sum \infty \frac{n}{1 + 8 n ^{3}}

n = 1 \sum \infty 10

n = 1 \sum \infty \frac{2 n}{3 n + 5}

What is the sum from n=0 to infinity of 8(1/10)^n ?
The sum from n=0 to infinity of 8(1/10)^n is 80/9