- You can not find an infinite sum for an arithmetic series.
- Geometric series where |r| < 1 are the only series that have an infinite sum.
- Formula: S = t1/1-r
- Set |r| < 1 and solve for x when you are finding infinite geometric converges.
- When you are writing a repeating decimal as a fraction you do this formula: repeating/place - 1.
Example 1: What is the fraction form of this decimal? .36363636
- First you have to find the number that is repeating: 36
- Now you follow the formula: repeating/place -1
- 36/100-1 (you put 100 because the first 36 is in the 100th place)
- You would then end up with 36/99
- Final answer: 36/99
Example 2: What is the sum of the infinite geometric series: 36 - 12 + 4 - . .
- First you must know that from the formula in the above notes, S stands for the sum.
- T1 is the first term that you are given in the series which is 36
- R is the number that is being multiplied to get to the next number which is -3. It is- 3 because 36/-12 = 3 and -12/4 = -3.
- Now you can plug the numbers into the formula.
- Formula: S = t1/1 - r.
- S = 36/1 - (.3) = 36/4 = 9
- Final answer: S = 9
- Amber :)
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