What is the sum from n=0 to infinity of 83(1/100)^n ?

The sum from n=0 to infinity of 83(1/100)^n is 8300/99

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sum from n=0 to infinity of 83(1/100)^n

n = 0 \sum \infty 83 (\frac{1}{100})^{n}

\frac{8300}{99}

Decimal

83.83838 \dots

Solution steps

n = 0 \sum \infty 83 (\frac{1}{100})^{n}

Apply the constant multiplication rule:

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

= 83 \cdot n = 0 \sum \infty (\frac{1}{100})^{n}

Apply Series Geometric Test:

\frac{100}{99}

= 83 \cdot \frac{100}{99}

Simplify

83 \cdot \frac{100}{99} : \frac{8300}{99}

= \frac{8300}{99}

What is the sum from n=0 to infinity of 83(1/100)^n ?
The sum from n=0 to infinity of 83(1/100)^n is 8300/99