| Infinite Series |
Find the sum of the following infinite series:
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Problem Moderated by: Douglas |
| Problem Solution |
This problem falls apart fairly nicely--if you see the pattern in the numerator:
1 = 31 - 21
5 = 32 - 22
19 = 33 - 23 ... etc.
The pattern in the denominator is much more obvious, being just the powers of 6.
So the series is actually the difference between two series:
f(x) = 3x/6x = 1/2x
g(x) = 2x/6x = 1/3x
These are both simple geometric series whose sums are 1, and 1/2.
Thus, the sum of the original series is 1 - 1/2 =1/2 |
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