当n趋向于无穷时,求下列式子的极限（（4n）!×n!)÷（（2n)!×（3n)!)

Question

当n趋向于无穷时,求下列式子的极限（（4n）!×n!)÷（（2n)!×（3n)!)

Answer 1

n→∞lim[(4n)!×n!]÷[(2n)!×(3n)!)
=n→∞lim[(4^n)×n!×n!]÷[(2^n)×n!×(3^n)×n!]
=n→∞lim[(4^n)]÷[(2^n)×(3^n)]
=n→∞lim[4÷(2×3)]^n
=n→∞lim[2/3]^n
=n→∞lim[1/1.5^n]
=0