+0

0
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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.

Jun 2, 2020
edited by lokiisnotdead  Jun 2, 2020

#1
+2

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

Jun 2, 2020
#2
+713
0

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

#3
+25500
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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

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

Jun 3, 2020