MathCastle
Counting & ProbabilityEasyIdentities and Techniques, Proved

Identities and Techniques, Proved · Easy problem

For which positive integer nn is

(55)+(65)+(75)+⋯+(n5)=(136) ?\binom{5}{5}+\binom{6}{5}+\binom{7}{5}+\cdots+\binom{n}{5}=\binom{13}{6}\,?