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jmc

algebra senior

Problem

Evaluate the infinite geometric series:

\frac{3}{2} - \frac{2}{3} + \frac{8}{27} - \frac{32}{243} + \dots

Solution

The series has first term

\frac{3}{2}

and common ratio

\frac{- 4}{9}

, so the formula yields:

\frac{\frac{3}{2}}{1 - ( \frac{- 4}{9} )} = \frac{27}{26}

.

Final answer

\frac{27}{26}