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Pretty sure the answer is 2/3. The question is equivalent to finding the probability that n(n+1) is divisible by 3. This occurs precisely when n is congruent to 0 or 2 mod 3. EDIT. You noticed this already, cool.

Neither.

I have a digital library of ridiculous proportions.

Pender >> Coroneos.

Well the n=2 case is enough to kickstart an induction, but I don't know if you would call that a circle geometry proof then.

That is not the general AM-GM. And there is a good reason why mathematicians don't like to use geometry to prove things like AM-GM, it turns out geometry is much harder to axiomatise.

This is an incredible achievement, especially if the proof is verified!

luls.

it wasn't a coincidence.

Haha maybe...

Its a worthwhile investment I feel.

And the word of god is always true, because the bible says so.

https://www.kigu.me/, http://www.kigurumicostumeshop.com.au/products-page/, there are a few other sites I think that source from the same people. Can't remember which one I bought from but prices are all around the same.

;). You should get one though, they are pretty amaze.

Haha it was ridiculously comfortable.

Oh right, you were talking about asymptotics. When you said limits = armwrestles I was thinking you were using the word in its most general sense...i.e. convergence. In terms of which functions dominate others, an armwrestle IS a good way to think of things. As an exercise in this concept, try...

Rocking my koala onesie.

Haha I have to admit I don't understand limits when you put it like that.

It should be something like that but there are a several possible conventions and they certainly don't touch upon this in high school. In higher mathematics the most common convention would probably be to define z^w = exp(w*Log(z)). Where Log(z)=log |z| + i*Arg(z) and -pi < Arg(z) =< pi...

It should be something like that but there are a several possible conventions and they certainly don't touch upon this in high school. In higher mathematics the most common convention would probably be to define z^w = exp(w*Log(z)). Where Log(z)=log |z| + i*Arg(z) and -pi < Arg(z) =< pi...