SOLUTION: Find the sum of the first ten terms of the geometric series 2-1+½-¼+...

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Question 1106812: Find the sum of the first ten terms of the geometric series 2-1+½-¼+...
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I personally don't like the formula for the sum of a finite geometric series; for most problems of this type I just do the arithmetic, if the numbers make it practical.

Since this is an alternating series, it simplifies things to group the terms in pairs.

2-1=1; 1%2F2-1%2F4+=+1%2F4; etc.

So the sum of 10 terms of the given geometric series is the sum of 5 terms of this new geometric series:

1+%2B+1%2F4+%2B+1%2F16+%2B+1%2F64+%2B+1%2F256
%28256%2B64%2B16%2B4%2B1%29%2F256
341%2F256