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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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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