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  1. Mar 13th, 2003, 08:23 PM #1
    sql_lall
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    Can anyone find a pattern?

    (For pattern, see a few posts down)

    In school we are just learning about the root of quadratics (sum= -b/a, product = c/a etc)
    There are many questions we have to do with stuff like: The roots of the equation "..." are A and B. Find the equation with roots 1/A3 and 1/B3
    This lead to a lot of stuffing about writing stuff in terms of (A+B) and AB. I then looked for a general formula, and found this:

    An+Bn =

    Code:
     
    k=n
    ___
Sn -\  (-1)k(P)k-1(S)n-2k+2 * [(n-k)C(k-2) + (n-k+1)C(k-1)]
    /__
    k=2
    where P(roduct) = AB, S(um) = A+B

    What i was wondering was:
    a) Can anyone proove/disproove this?
    b) can (n-k)C(k-2) + (n-k+1)C(k-1) be simplified?
    Last edited by sql_lall; Apr 9th, 2003 at 06:10 PM.
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