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Square Sequence (Posted on 2003-12-19) Difficulty: 5 of 5
When you add all the terms up from this sequence: x + (x-1) + 3(x-2) + (x-3) + (x-4) + (x-5) + 3(x-6) + (x-7) ... it will be equal to half of (x + x - x) for any positive even integer x. Prove why this works.

Example: 12 + 11 + 10 + 10 + 10 + 9 +8 + 7 + 6 + 6 + 6 + 5 + 4 + 3 + 2 + 2 + 2 + 1 if x = 12.

Note: The coefficients go 1, 1, then 3, then 3 1s, then 3, then 3 1s. The coefficients go in this order, even if there are coefficients left when the sequence stops. For example, with 6, the coefficients would go 1,1,3,1,1,1.

See The Solution Submitted by Gamer    
Rating: 2.5000 (4 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
More about approachGamer2007-02-19 15:37:37
different approachLee2003-12-22 06:54:26
re: Sorry, my mistakeGamer2003-12-20 20:41:47
Sorry, my mistakePenny2003-12-20 10:39:36
re(3): proofGamer2003-12-20 07:36:11
Some Thoughtsre(2): proofPenny2003-12-20 00:13:13
re: proofGamer2003-12-19 18:27:34
SolutionproofCharlie2003-12-19 16:33:44
SolutionSolution (no computer assistance used)Penny2003-12-19 15:33:16
if x=3???rerun1412003-12-19 12:38:22
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