+0  
 
0
188
3
avatar+732 

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! :))

 Jun 2, 2020
edited by lokiisnotdead  Jun 2, 2020
 #1
avatar
+2

Just add 1 to the last term (both top and bottom) !.

 Jun 2, 2020
 #2
avatar+732 
0

thank you so much!!! that really helped!!!!

lokiisnotdead  Jun 3, 2020
 #3
avatar+25574 
+2

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

 

\(\dbinom{13}{13} + \dbinom{14}{13} + \dbinom{15}{13} + \dots + \dbinom{52}{13} + \dbinom{53}{13} + \dbinom{54}{13} = \dbinom{55}{14}\)

 

laugh

 Jun 3, 2020

43 Online Users

avatar