+738 Let n and k be positive integers such that \(n<10^6\) and
\(\binom{13}{13} + \binom{14}{13} + \binom{15}{13} + \dots + \binom{52}{13} + \binom{53}{13} + \binom{54}{13} = \binom{n}{k}.\)
Find the value of n and k.
thanks and please help! i only need hints, i don't need the full answer! :))
+26393 Let n and k be positive integers such that n<10^6 and
\(\dbinom{13}{13} + \dbinom{14}{13} + \dbinom{15}{13} + \dots + \dbinom{52}{13} + \dbinom{53}{13} + \dbinom{54}{13} = \dbinom{n}{k}\).
Find the value of n and k.
see Hockey-stick identity: https://en.wikipedia.org/wiki/Hockey-stick_identity
\(\dbinom{13}{13} + \dbinom{14}{13} + \dbinom{15}{13} + \dots + \dbinom{52}{13} + \dbinom{53}{13} + \dbinom{54}{13} = \dbinom{55}{14}\)
