We're doing a factorial proof in class and I need some help. I'm normally pretty solid in math, but I'm just not seeing this one.
It is basically Pascal's triangle. Two consecutive numbers on one row summed together will equal the number directly below. We have to determine this in terms of n and r.
n! (n-1)! (n-1)!
----------- = ------------ + --------------
r! x (n-r)! (r-1)! x ((n-1)-(r-1))! r! x ((n-1)-r))!
where n is the number of rows down from the top of the triangle starting with zero at the top. r is the number from left to right starting from zero. So you have to do n-1 to get to the row above and r-1 to get to the number to the left of the number. Regular r would get you the second consecutive number a row up. I know you would distribute the negative sign in the denominator of the first term (I guess). I have also tried to get common denominators and it just will not work for me.
I am at school right now and the proof is due tomorrow so any help would be appreciated. I know this kind of stuff sux to type out, so if someone could just write out the procedures that be cool.
Thanks
Jerry Berger
It is basically Pascal's triangle. Two consecutive numbers on one row summed together will equal the number directly below. We have to determine this in terms of n and r.
n! (n-1)! (n-1)!
----------- = ------------ + --------------
r! x (n-r)! (r-1)! x ((n-1)-(r-1))! r! x ((n-1)-r))!
where n is the number of rows down from the top of the triangle starting with zero at the top. r is the number from left to right starting from zero. So you have to do n-1 to get to the row above and r-1 to get to the number to the left of the number. Regular r would get you the second consecutive number a row up. I know you would distribute the negative sign in the denominator of the first term (I guess). I have also tried to get common denominators and it just will not work for me.
I am at school right now and the proof is due tomorrow so any help would be appreciated. I know this kind of stuff sux to type out, so if someone could just write out the procedures that be cool.
Thanks
Jerry Berger
