20121127, 18:14  #1 
I quite division it
"Chris"
Feb 2005
England
31·67 Posts 
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? *Define as appropriate. 
20121127, 18:55  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3^{2}·1,117 Posts 
WolframAlpha is really good for oneoffs: 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 tries 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. 
20121127, 20:11  #3 
"Nathan"
Jul 2008
Maryland, USA
10001011011_{2} Posts 
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 "SIXTYFOUR! over THIRTYTWO!". 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. 
20121127, 20:43  #4 
Jul 2003
So Cal
2^{2}×11×59 Posts 
Breaking it down, I first notice that and are both 0, so those terms drop out. Then, . Next, and are both 0, so is simply 1. Thus we conclude that this was constructed by a joker trying to be cute.
We are then left with . This becomes clear one you write out a few terms of the expansion. 
20121128, 02:22  #5  
Romulan Interpreter
"name field"
Jun 2011
Thailand
10274_{10} Posts 
Quote:
Quote:
Last fiddled with by LaurV on 20121128 at 02:23 

20121128, 16:51  #6 
I quite division it
"Chris"
Feb 2005
England
31·67 Posts 
I pronounce these as 'sixtyfour pling', like a rather depressed microwave. Don't know where I picked that up.

20121128, 20:55  #8 
"Nathan"
Jul 2008
Maryland, USA
1115_{10} Posts 
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!?

20121128, 21:26  #9 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 

20121128, 21:36  #10 
"Ben"
Feb 2007
7×13×41 Posts 
Generalizing to any m! with n least terms missing:

20121128, 22:18  #11 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3^{2}×1,117 Posts 
Relevant to PE 403, try this:
Sum(over odd d from d_{1} to d_{2}) (2 + (d^{3}+5d)/3) and the same for even d values. 
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