Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


MJ
Posts:
10
Registered:
4/21/05


Re: Small but powerful triangles
Posted:
Apr 21, 2005 8:50 AM


"amcwill417" <amcwill417@email.msn.com> wrote in message news:JPw9e.7$S23.465@eagle.america.net...
> All positive integers. Suppose (k)^n + (k+1)^n > (k+2)^n. What about an > explicit expression (in terms of n) for the smallest value of k for which > this is true (for any given n)? > Alex
(k)^n + (k+1)^n > (k+2)^n.
Equivalently,
(x1)^n + x^n > (x+1)^n
(x+1)^n  (x1)^n < x^n
d/dx (2*x^n) < x^n
2n*x^(n1) < x^n
x > 2n
So the answer is around 2n.
MJ



