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# Algebra

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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.

Jan 7, 2022

$$1+\left(\frac{1}{8}\right)+\left(\frac{1}{8}\right)^2 + \left(\frac{1}{8}\right)^3 + \dots = \displaystyle\sum_{n=1}^{\infty} 8^{1-n} = \frac{8}{7}$$