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Powered Greatest Root (Posted on 2011-02-03) Difficulty: 3 of 5
The sequence {An, n ≥ 0} is defined by:

A0 = 0, and:

An+1 = [3√(An + n)]3

Determine an explicit formula representing An in terms of n.

Hence, or otherwise, determine all n such that An = n

Note: [x] represents the greatest integer ≤ x

No Solution Yet Submitted by K Sengupta    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution via research and quad formula, with a fudge for n=1 Comment 4 of 4 |
(In reply to solution via research and quad formula, with a fudge for n=1 by Charlie)

Thanks for the explanation!

Does it follow that the An = n iff n={8,27}? With the larger values An seems to be increasing beyond n's ability to catch up.


  Posted by broll on 2011-02-04 03:34:23
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