# [SOLVED] urgent!! prove using binomial throrem

• Sep 9th 2007, 01:48 PM
bdou
[SOLVED] urgent!! prove using binomial throrem
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!
• Sep 9th 2007, 02:04 PM
Plato
$\begin{array}{l}
\left( {x + y} \right)^n = \sum\limits_{k = 0}^n {_n C_k } x^k y^{n - k} \\
\end{array}
$
• Sep 10th 2007, 01:40 AM
red_dog
For the second one:
$\displaystyle (x-y)^n=\sum_{k=0}^n(-1)^kC_n^kx^{n-k}b^k$ and set $x=y=1$