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Two Geometric Series (Posted on 2003-07-14) Difficulty: 2 of 5
Find a geometric series of 3 or more positive integers, starting with 1, such that its sum is a perfect square.

See if you can find another such series.

See The Solution Submitted by Brian Smith    
Rating: 3.6667 (6 votes)

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Some Thoughts Starters | Comment 2 of 10 |
The sum of the first n terms of a geometric series is:

Sn = t1(1-r^n)/(1-r)

where t1 is the first term and r is the common ratio (and not 0).

Since this problem specifies that t1=1, we need to find a solution for

Sn = (1-r^n)/(1-r) = x²

where x, r, and n are all integers.

I haven't time to complete it now (back to work!), but that is where I think we need to start.
  Posted by DJ on 2003-07-14 06:43:22
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