Fluffy Posted February 2, 2009 Report Share Posted February 2, 2009 I have the series 1/1 * 2/3 * 3/5 * 4/7 * 5/9.... The first part is obviously N!, but I can't find how to note the lower part in an elegant way, is there any? Quote Link to comment Share on other sites More sharing options...
rogerclee Posted February 2, 2009 Report Share Posted February 2, 2009 zero Quote Link to comment Share on other sites More sharing options...
P_Marlowe Posted February 2, 2009 Report Share Posted February 2, 2009 Depends, what you understand under elegant. There exists a symbol for a product, the big greek letter for Pi, <PI> (n/(2n-1)) from N=1 to N=??? or <PI> ((n+1)/(2n+1)) from N=0 to N=??? the latter may be better, because it starts with zero, but maybe youbelong to the camp, which claims, that 0 is not a natural number .-). The PI symbol is the aequivalent to the sigma symbol for sums. The above formula is at least compact. Additional, there may be a formular using combinatoric symbols,I am away from math since more than 10 years agao, so I amtoo rusty, but it sould be possible to find a compact formula, ifyou dont want to use the product symbol. With kind regardsMarlowe Quote Link to comment Share on other sites More sharing options...
david_c Posted February 2, 2009 Report Share Posted February 2, 2009 I have the series 1/1 * 2/3 * 3/5 * 4/7 * 5/9.... The first part is obviously N!, but I can't find how to note the lower part in an elegant way, is there any? If you're just looking for a way to write 1 x 3 x 5 x ... x (2n-1), then you can do this by (2n)! / (2^n)n!. But if you're actually trying to write the series, then do what PMarlowe said. Quote Link to comment Share on other sites More sharing options...
Fluffy Posted February 2, 2009 Author Report Share Posted February 2, 2009 2n! / (2^n)n! that's what I was looking for, I could feel there was something like that. Thx David. Quote Link to comment Share on other sites More sharing options...
JLOL Posted February 2, 2009 Report Share Posted February 2, 2009 zero LOL Quote Link to comment Share on other sites More sharing options...
gwnn Posted February 2, 2009 Report Share Posted February 2, 2009 erm! I am pretty sure I have learned something about n!! being only the odd or even numbers of the factorial terms. It might have been just a theoretical physics notation for lazy people. edit: found it on wikipedia, n!! is either the odd or the even terms, depending if n is odd or even. 4!!=2*47!!=1*3*5*7 Quote Link to comment Share on other sites More sharing options...
david_c Posted February 2, 2009 Report Share Posted February 2, 2009 erm! I am pretty sure I have learned something about n!! being only the odd or even terms of the factorial terms. Yep. That's a standard notation, though I think it's one of those things that you wouldn't use in a paper without explaining what it means. (Whereas with the simple factorial n! it's safe to assume people know what you're talking about.) Quote Link to comment Share on other sites More sharing options...
Walddk Posted February 2, 2009 Report Share Posted February 2, 2009 (Whereas with the simple factorial n! it's safe to assume people know what you're talking about.) I just realised that I do not belong to "people" :blink: Roland Quote Link to comment Share on other sites More sharing options...
P_Marlowe Posted February 2, 2009 Report Share Posted February 2, 2009 (Whereas with the simple factorial n! it's safe to assume people know what you're talking about.) I just realised that I do not belong to "people" :blink: Roland Me neither. I have never seen n!!. But than I only listed to very few lectures about number theory. Maybe the term regular pops up in certain series relevant for physics,Bernoulli Function or something similar? With kind regardsMarlowe Quote Link to comment Share on other sites More sharing options...
helene_t Posted February 2, 2009 Report Share Posted February 2, 2009 zero LOL "Zero" was my first thought also but of course it should be understood as a finite product. Quote Link to comment Share on other sites More sharing options...
kenberg Posted February 2, 2009 Report Share Posted February 2, 2009 (Whereas with the simple factorial n! it's safe to assume people know what you're talking about.) I just realised that I do not belong to "people" :P Roland I feel your pain. I was once at a party where most of the guests were graduate students in the French Department, all speaking French. They could not understand why I left early, although when I said adios, amigos, that might have been a clue. Quote Link to comment Share on other sites More sharing options...
Fluffy Posted February 2, 2009 Author Report Share Posted February 2, 2009 ok, there is a notation for this Thanks Csaba. I atually prefer david's first suggestion because I have another 1/2^N that goes away with this one. (Wich I actually should have suspected given that the results of the first Ns dome manually didn't show 2^N anywhere) This all comes because in my poker forum they started to talk about mathematic problems. There was a guy who proposed the problem, then rejected my solution wich is actually right LOL. Quote Link to comment Share on other sites More sharing options...
gwnn Posted February 3, 2009 Report Share Posted February 3, 2009 zero LOL "Zero" was my first thought also but of course it should be understood as a finite product. 1*3*5*7*9*... = zero when the terms grow indefinitely? :rolleyes: Quote Link to comment Share on other sites More sharing options...
kenberg Posted February 3, 2009 Report Share Posted February 3, 2009 ok, there is a notation for this Thanks Csaba. I atually prefer david's first suggestion because I have another 1/2^N that goes away with this one. (Wich I actually should have suspected given that the results of the first Ns dome manually didn't show 2^N anywhere) This all comes because in my poker forum they started to talk about mathematic problems. There was a guy who proposed the problem, then rejected my solution wich is actually right LOL. Implicit in what you are saying: The best form for an expression often depends greatly on what you are going to do next. Quote Link to comment Share on other sites More sharing options...
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