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Binomial Expansion - HELP! (1 Viewer)

TooF

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Jan 6, 2004
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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!
 

TooF

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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

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

coca cola

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

withoutaface

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(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 :)
 

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