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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
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But the sum of the first series is:
1744940226888640731855880375380
While the square of your root is:
1744940226888640555371025544169

The sum of your second series is:
1291911066888533017939127925460
While the square is:
1291911066888532717237377152400

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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