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 Let n and k be positive integers such that n < 10^6 and \[\binom{13}{13} + \binom{14}{13} + \binom{15}{13} + \dots + \binom{52}{13} + \binom{53}{13} + \binom{54}{13} = \binom{n}{k}.\]Enter the ordered pair (n,k).

 Jun 21, 2020
 #1
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The sum adds up to 707,285,522,570 = C(57,12), so (n,k) = (57,12).

 Jun 22, 2020
 #2
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Let n and k be positive integers such that n<10^6  and
\(\dbinom{13}{13} + \dbinom{14}{13} + \dbinom{15}{13} + \dots + \dbinom{52}{13} + \dbinom{53}{13} + \dbinom{54}{13} = \dbinom{n}{k}\)

 

See Rom: https://web2.0calc.com/questions/let-n-and-k-be-positive-integers-such-that-and-what
My answer see: https://web2.0calc.com/questions/please-help_24682

 

laugh

 Jun 22, 2020

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