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# Find the sum of the following infinite geometric series, if it exists. 1/3+1/9+1/27+1/81+...

The given infinite geometric series is $\frac{1}{3},\, \frac{1}{9}, \, \frac{1}{27} , \, \frac{1}{81} , \, ...,$ The first term is a = 1/3. The common ratio is r = 1/3. The sum is $\frac{a}{1-r}= \frac{1/3}{1 - 1/3} = \frac{1}{2}$ Answer:  1/2