SOLUTION: What is the sum of this infinite geometric series 1-1/3+1/9-...

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Question 1013967: What is the sum of this infinite geometric series 1-1/3+1/9-...
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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What is the sum of this infinite geometric series  1 - 1/3 + 1/9 - . . .
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The first term is  1.
The common ratio is  -1%2F3.

Now apply the formula for the sum of an infinite geometric progression with the first term  a  and the common ratio  r,  |r| < 1 :

S = a%2F%281-r%29.

So,  in our case

S = 1%2F%281-%28-1%2F3%29%29 = 1%2F%28%284%2F3%29%29%29 = 3%2F4%29.