SOLUTION: Find the exact fraction value foe the number 0.123123123....... using series only.

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Question 9823: Find the exact fraction value foe the number 0.123123123....... using series only.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
not sure what you mean "by Series". The only way i am aware is to do the following:

look at the repeating part, which here is 123. We need one whole section in front of the decimal point, so we need to multiply by 1000...

let r = 0.123123123...
so 1000r = 123.123123123...

now subtract the first from the second, leaving 999r = 123

so r = 123/999

jon