Find the sum of the following infinite geometric series, if it exists. 1/3+1/9+1/27+1/81+...
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Answer:
- <u><em>All real numbers except c = 0 and c = 3.</em></u>
Explanation:
The equation is:
Since c - 3, c, and c(c - 3) are he denominators, none of them can be equal to zero:
- c ≠ 0
- c - 3 ≠ 0 ⇒ c ≠ 3
- c (c - 3) ≠ 0 ⇒ c ≠ 0 and c ≠ 3.
Now you can multiply both sides of the equation by the common denominator: c (c - 3):
That means the equality is valid for all real numbers for which it is defined, which is all real numbers except c = 0 and c = 3.