SOLUTION: Write the following as a summation and find the sum of the series (3-1)+(1/3-1/9)+....

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Question 749911: Write the following as a summation and find the sum of the series (3-1)+(1/3-1/9)+....
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
If (3-1)+(1/3-1/9)+.... is an infinite geometric series then it is equal to:
sum%28+3%281%2F9%29%5En+-+%281%2F9%29%5En%2C+n+=+0%2C+infinity%29+.
The sum of an infinite geometric series with first term a%5B1%5D
and common ratio r is equal to a%5B1%5D%2F%281-r%29 provided that |r| < 1.
sum%28+3%281%2F9%29%5En+-+%281%2F9%29%5En%2C+n+=+0%2C+infinity%29+ = %283+-+1%29%2F%281-%281%2F9%29%29 = highlight%282.25%29