# Long Sequences...

Discrete Mathematics Level 3

If $\frac {\binom{n}{r}+ 4 \binom{n}{r+1} + 6 \binom{n}{r+2} + 4 \binom{n}{r+3} + \binom{n}{r+4}}{\binom{n}{r} + 3 \binom{n}{r+1} + 3 \binom{n}{r+2} +\binom{n}{r+3}} = \frac{n + k}{r + k}$ then the value of k is