If three successive terms of a geometric sequence with ratio r correspond to the lengths of the three sides of a triangle, then determine whether or not [r]+[-r]=-1.

[x] is the greatest integer ≤ x.

(In reply to Quick spoiler by e.g.)

The formula actually works for all noninteger r, but in a triangle we could have r=1, so the answer should be "Almost always true."

For integer r, [r]=-[-r], so the sum is 0, not -1.

Posted by Old Original Oskar! on 2007-03-19 08:47:32