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

The sum from n=0 to infinity of 5/(10^n) is 50/9

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

n = 0 \sum \infty \frac{5}{1 0 ^{n}}

\frac{50}{9}

Solution steps

n = 0 \sum \infty \frac{5}{1 0 ^{n}}

Apply the constant multiplication rule:

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

= 5 \cdot n = 0 \sum \infty \frac{1}{1 0 ^{n}}

Apply Series Geometric Test:

\frac{10}{9}

= 5 \cdot \frac{10}{9}

Simplify

5 \cdot \frac{10}{9} : \frac{50}{9}

= \frac{50}{9}

k = 1 \sum \infty \frac{k}{ln ( k )}

n = 1 \sum \infty \frac{7 ^{n}}{n ! n}

n = 0 \sum \infty 8 (\frac{1}{9})^{n}

n = 0 \sum \infty e^{- 18 n}

k = 1 \sum \infty (\frac{2}{3})^{k}

What is the sum from n=0 to infinity of 5/(10^n) ?
The sum from n=0 to infinity of 5/(10^n) is 50/9