why is "nCk+nCk-1" equal to "n+1Ck" ?

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- Feb 1st 2013, 11:10 PMmikicombination
why is "

*nCk*+*n**C**k-1*" equal to "*n+1**C**k*" ?

- Feb 2nd 2013, 12:03 AMjakncokeRe: combination
Algebriacally, well Assume

Observe that (1)

so (i can do this since k/k = 1)

(im using (1) )

multiply the first equation by to get both denominaters equals

which equals

which is n+1 C k.