Binomial coefficient proof Prove that for any $0\lt r\lt n$ we have $$\binom nr=\binom{n-1}{r-1}+\binom{n-1}r.$$
How do prove this and what step do i take in order for it to be true? 

This is simple. $(_r^n)$ corresponds to the number in the $(r+1)$th position of the $(n+1)$th row of pascal's triangle. Pascal's triangle is generated by, for each position, adding the numbers in the positions above it, which happen to be $(_{r-1}^{n-1})$ and $(_r^{n-1})$. 
