Weird limits

Calculus Level 5

Let \[ \lim _{ n\rightarrow \infty }{ \binom{n}{7} { p }^{ r }{ q }^{ n-r } }=\frac {{e}^{A}.{B}^{C}}{D!}\ \]

Find \(A\)+\(B\)+\(C\)+\(D\)


  • Given: \(p+q=1\) and \(np=5\).
  • Bonus: Generalize for r and m in place of 7 and 5 respectively.
  • Notation: \(\binom{n}{r}=\frac{n!}{(n-r)!r!}\)
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