[SOLVED] urgent!! prove using binomial throrem

bdou · September 9th 2007, 01:48 PM

hey! i have a question from my number theory worksheet.

prove that nC0+nC1+nC2+...+nCn=2^n and
nC0-nC1+nC2-...+(-1)^n(nCn)=0

it hints to use the binomial theorem
any help would be amazing!

**Plato** · September 9th 2007, 02:04 PM

$\begin{array}{l}<br /> \left( {x + y} \right)^n = \sum\limits_{k = 0}^n {_n C_k } x^k y^{n - k} \\ <br /> \mbox{Let}\quad x = 1\quad \& \quad y = 1 \\ <br /> \end{array}<br />$

**red_dog** · September 10th 2007, 01:40 AM

For the second one:
$\displaystyle (x-y)^n=\sum_{k=0}^n(-1)^kC_n^kx^{n-k}b^k$ and set $x=y=1$

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