Evaluate the infinite geometric series: 13+16+112+124+

The series has first term 13 and common ratio 12, so the formula yields: 131-(12)=23.

jmc

algebra intermediate

Problem

Evaluate the infinite geometric series:

\frac{1}{3} + \frac{1}{6} + \frac{1}{12} + \frac{1}{24} + \dots

Solution

The series has first term

\frac{1}{3}

and common ratio

\frac{1}{2}

, so the formula yields:

\frac{\frac{1}{3}}{1 - ( \frac{1}{2} )} = \frac{2}{3}

Final answer

\frac{2}{3}