The sequence {A_n, n ≥ 0} is defined by:

A₀ = 0, and:

A_n+1 = [³√(A_n + n)]³

Determine an explicit formula representing A_n in terms of n.

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

Note: [x] represents the greatest integer ≤ x

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