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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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Question Question? | Comment 1 of 4

Not sure I follow this as it looks suspiciously straightforward for a '3'.

((x+y)^(1/3))^3 is just a long-winded way of saying (x+y), equivalent in this case to n(n+1)/2, while (x^(1/3)+y)^3 is equivalent to (n(n+1)/2)^3. so it is either the triangular numbers or the cube of the triangular numbers.

Am I missing something?

Is there a problem with the problem?

  Posted by broll on 2011-02-03 13:48:13
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