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

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

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sum from n=0 to infinity of 9/(10^n)

n = 0 \sum \infty \frac{9}{1 0 ^{n}}

10

Solution steps

n = 0 \sum \infty \frac{9}{1 0 ^{n}}

Apply the constant multiplication rule:

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

= 9 \cdot n = 0 \sum \infty \frac{1}{1 0 ^{n}}

Apply Series Geometric Test:

\frac{10}{9}

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

Simplify

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

= 10

n = 0 \sum \infty 1 0^{n}

n = 1 \sum \infty (\frac{11}{5})^{n}

k = 1 \sum \infty \frac{1}{1 1 ^{k}}

n = 1 \sum \infty \frac{( 1 - 3 ) ^{n}}{n}

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

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