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jmc

algebra senior

Problem

Evaluate the infinite geometric series:

1 - \frac{2}{7} + \frac{4}{49} - \frac{8}{343} + \dots

Solution

The series has first term

1

and common ratio

\frac{- 2}{7}

, so the formula yields:

\frac{1}{1 - ( \frac{- 2}{7} )} = \frac{7}{9}

.

Final answer

\frac{7}{9}