Binomial Expansion - HELP! (1 Viewer)

[TooF]

How do you prove

(n-1)Ck + (n-1)C(k-1) = nCk

????

It looks a bit messy, but I'm assuming that you'll be able to write it out properly on paper? Thanks! This is pretty urgent, exms tomorrow!

 

[nick1048]

sub a different pro numeral for Ck, say x for instance and clean up the algebra...

 

[TooF]

This isn't an algebra question though - its the binomial theorem
you can't just stick in an x in place of Ck

(or can you? :S)

 

[Supra]

dont u just use the fact that nCk= n!/k!(n-k)! and manipul8 both sides

 

[coca cola]

you can find a simple proof in math in focus, page 424 if you got the new ed.

 

[withoutaface]

(n-1)!/[k!(n-1-k)!]+(n-1)!/[(k-1)!(n-k)!]=n!/[k!(n-k)!]
n-k+k=n multiply both sides by (n-1)!/[k!(n-k)!]
n=n, as required