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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Programming Solution | Comment 8 of 10 |
(In reply to Programming Solution by DJ)

Unfortunately, it appears that your program suffers from precision problems. Since Math.sqrt and Math.pow are most likely floating point operations, their precission is limited.
Your first two "big" solutions are:

r=11, n=30, root=1320961856712237
r=13, n=28, root=1136622658092180

But the sum of the first series is:
While the square of your root is:

The sum of your second series is:
While the square is:

So it still looks like there are no further solutions after the first two, but of course such things need to be proved mathematically.
  Posted by exoticorn on 2003-07-14 22:41:33

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