Playing with WolframAlpha and musing.
 

As someone who really struggles with maths I am interested in what a person with a 'good mathematical understanding'* sees when they look at something like this.

Do they look at this and just understand or is this not obvious to such a person?

:smile:
*Define as appropriate.

WolframAlpha is really good for one-offs: say you don't want to derive (and don't remember by heart) Sum(0<=i<=n)i^3, then it will tell you!
However, with a little more obscure requests, it gives you some fluff, i.e. it [I]tries[/I] to be helpful and applies every possible diversion, and every once in a while is been almost sarcastic (it would seem ;-) to the point of being absurd.

I have an advanced degree in math(s), if that counts, and I can tell you that the "simplification" provided by Alpha is something that no one (outside of a student trying to be a smart aleck) would ever make serious use of. It would be akin to asking for a glass of "aqueous dihydrogen monoxide" rather than "water". I suspect that it is an example of the computer's AI scheme running amok.

On the other hand, at least it didn't reply to 64!/32! by loudly chanting "SIXTY-FOUR! over THIRTY-TWO!". There was a guy in a *college* class of mine that actually saw 3! and pronounced it "THREE!" and wondered why they wanted us to shout the numbers.

Breaking it down, I first notice that [TEX]-1+\cos(128\pi)[/TEX] and [TEX]-1+\cos(64\pi)[/TEX] are both 0, so those terms drop out. Then, [TEX]2^{-64}/2^{-32} = 1/2^{32}[/TEX]. Next, [TEX]\sin(64\pi)[/TEX] and [TEX]\sin(32\pi)[/TEX] are both 0, so [TEX]\pi^0[/TEX] is simply 1. Thus we conclude that this was constructed by a joker trying to be cute.

We are then left with [TEX]\frac{64!}{32!}=\frac{128!!}{64!! \times 2^{32}[/TEX]. This becomes clear one you write out a few terms of the expansion.

[QUOTE=NBtarheel_33;319770]There was a guy in a *college* class of mine that actually saw 3! and pronounced it "THREE!" and wondered why they wanted us to shout the numbers.[/QUOTE]

(this is cool, I have to remember it! :smile:)

[QUOTE=frmky;319771]
We are then left with [TEX]\frac{64!}{32!}=\frac{128!!}{64!! \times 2^{32}[/TEX]. This becomes clear one you write out a few terms of the expansion.[/QUOTE]

According with the former, the last should be [SIZE=6]ONE HUNDRED TWENTY EIGHT!! [/SIZE]etc...
:rofl: :razz: :ouch2:

I pronounce these as 'sixty-four [I]pling[/I]', like a rather depressed microwave. Don't know where I picked that up.

Many people would maybe use a '[URL="http://en.wikipedia.org/wiki/Alveolar_click"]click[/URL]' (although probably not English speakers), for example, the [URL="http://en.wikipedia.org/wiki/%C7%83Kung_language"]!Kung[/URL].

So, is there a symbol for "factorial missing the least n terms"? For instance, is there a notation for 64!/32! other than 64!/32!?

[QUOTE=NBtarheel_33;319870]So, is there a symbol for "factorial missing the least n terms"? For instance, is there a notation for 64!/32! other than 64!/32!?[/QUOTE]

[tex]\prod_{i=33}^{64}i[/tex] :smile:

Generalizing to any m! with n least terms missing:

[TEX]\prod_{i=m-n+1}^{m}i[/TEX]

:smile:

Relevant to PE 403, try this:
Sum(over odd d from d[SUB]1[/SUB] to d[SUB]2[/SUB]) (2 + (d[SUP]3[/SUP]+5d)/3)
and the same for even d values.