Thread: wikipedia entry on Pascal's rule

Hi

here is link to Pascal's rule at wikipedia

Pascal's rule - Wikipedia, the free encyclopedia

its written as



if we plug in k=n+1 , we get






is something wrong ?

i think the range should defined as



right ?

Originally Posted by issacnewton

i think the range should defined as



right ?

How would you define

?

It seems to involve (-1)! in the denominator which I'm sure Pascal would not approce of.

CB

thats what i was wondering.. is wikipedia entry wrong then ?

Originally Posted by issacnewton

thats what i was wondering.. is wikipedia entry wrong then ?

I beleive so, >>Planet Math's<< limits for k are what we might expect

I think I should also give >>Proof Wiki's<< page a plug.

CB

Thanks captain , So did you fix 'proof wiki' page. When I went there, it was ok. Ask somebody at wikipedia to fix it.

Originally Posted by issacnewton

Thanks captain , So did you fix 'proof wiki' page. When I went there, it was ok. Ask somebody at wikipedia to fix it.

Proof Wiki is nothing to do with Wikipedia, it is a site maintained by a sometime helper here on MHF.

CB

Some authors define

whenever it is not true that .

See, for example, Knuth, "The Art of Computer Programming, Vol 1", or
Binomial Coefficient -- from Wolfram MathWorld.

By this definition, it is correct to say that
.

if that is what the definition is , then all is well............

Originally Posted by issacnewton

if that is what the definition is , then all is well............

It is not the definition but a definition. Knuth is particularly known for this sort of thing (defining undefined notation in a manner which suits his current purpose), but it is also consistent with interpretation of the factorial in terms of the gamma function.

CB