Sorry I don't know how to type this in mathematical symbols.

Prove that:

the summation from r=0 to n of (C(n,r))(a-1)^r = a^n

Thanks for any help I can get

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- Oct 20th 2009, 09:22 AMbabbaganduCan't do combinatorial proofs. Can someone help?
Sorry I don't know how to type this in mathematical symbols.

Prove that:

the summation from r=0 to n of (C(n,r))(a-1)^r = a^n

Thanks for any help I can get - Oct 20th 2009, 09:39 AMPlato
Use the binomial theorem.

$\displaystyle \left( {x + y} \right)^n = \sum\limits_{r = 0}^n {\binom{n}{r}x^r y^{n - r} } $

Let $\displaystyle x=(a-1)~\&~y=1$