# How do you find the sum of the infinite geometric series 12+4+4/3+...?

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To find the sum of an infinite geometric series, use the formula for the sum:

[ S = \frac{a}{1 - r} ]

Where:

- ( a ) is the first term of the series
- ( r ) is the common ratio

For the given series ( 12 + 4 + \frac{4}{3} + \ldots ), the first term ( a = 12 ) and the common ratio ( r = \frac{1}{3} ).

Plug these values into the formula:

[ S = \frac{12}{1 - \frac{1}{3}} ]

[ S = \frac{12}{\frac{2}{3}} ]

[ S = 18 ]

So, the sum of the infinite geometric series ( 12 + 4 + \frac{4}{3} + \ldots ) is ( 18 ).

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