lean_workbook_plus_22580

For any $m<n$ , $\binom{n}{m+1}=\frac{n-m}{m+1}\binom{n}{m}$ , so $\binom{n}{m+1}<\binom{n}{m}$ if $m<\frac{n-1}2$ and $\binom{n}{m+1}>\binom{n}{m}$ if $m>\frac{n-1}2$.