+306 Let n and k be positive integers such that \(n<10^6\) and \(\binom{13}{13} + \binom{14}{13} + \binom{15}{13} + \dots + \binom{52}{13} + \binom{53}{13} + \binom{54}{13} = \binom{n}{k}\)
What is the ordered pair (n, k)?
+6250 \(\text{Using the hockey stick identity}\\ \sum \limits_{n=13}^{54}\dbinom{n}{13} = \dbinom{54+1}{13+1} = \dbinom{55}{14}\)
+306 oh that makes sense to use the hockey stick identity. Thanks for the help!!
