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# geometric series

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Calculate the sum of the geometric series $1+\left(\frac{1}{8}\right)+\left(\frac{1}{8}\right)^2 + \left(\frac{1}{8}\right)^3 + \dots$. Express your answer as a common fraction.

Jun 16, 2021

#1
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GP:  $$1, {1\over8}, {1\over 8^2},...$$

a = 1, r = 1/8

$${S}_{∞} ={a\over 1-r}$$

$$={1\over 1-{1\over 8}}$$

$$={8\over 7}$$

Jun 16, 2021