Hi

here is link to Pascal's rule at wikipedia

Pascal's rule - Wikipedia, the free encyclopedia

its written as

$\displaystyle \binom{n}{k}+\binom{n}{k-1}=\binom{n+1}{k} \;\mbox{for}\;1\le k\le n+1$

if we plug in k=n+1 , we get

$\displaystyle \binom{n}{n+1}+\binom{n}{n}=\binom{n+1}{n+1}$

$\displaystyle \Rightarrow \binom{n}{n+1}=0$

is something wrong ?