Omnimaga

General Discussion => Other Discussions => Math and Science => Topic started by: AngelFish on August 06, 2011, 01:36:42 am

Title: A little problem
Post by: AngelFish on August 06, 2011, 01:36:42 am

Here's a little ditty related to some stuff I've been working on. This problem has managed to crash Mathematica, confuse Matlab, destroy my attempts at a symbolic solution, and cause Wolfram Alpha to throw a temper tantrum. In short, it's a nasty little bugger and I was wondering if anyone else wanted to take a crack at it:

Lim_N→∞ N/(2^^{⌊Log₂N⌋})


+10 Math points to anyone who can either solve it or demonstrate that there's no elementary solution  :P

Title: Re: A little problem
Post by: phenomist on August 06, 2011, 04:06:28 am

No limit kind sir.

Consider N = 2^k, for arbitrarily large k. then the answer is 1.

Now consider N = 2^k-epsilon, for arbitrarily large k. then the limit is 2.

[note: k = integer]

undefined limit.

(note: have floors, abuse boundary conditions :P)

Title: Re: A little problem
Post by: AngelFish on August 06, 2011, 05:15:20 am

I suppose that should have been pretty obvious :P

Thanks.
/me hands over the promised +10 points