还是极限问题2利用夹逼定理计算极限lim(4^n+5^n+6^n)^1/n其中n趋向于无穷大

Question

还是极限问题2
利用夹逼定理计算极限
lim(4^n+5^n+6^n)^1/n 其中n趋向于无穷大

Answer 1

(4^n+5^n+6^n)^1/n ≤[3*6^n]^(1/n)
∴lim(4^n+5^n+6^n)^1/n ≤lim[3*6^n]^(1/n)=lim[3^(1/n)*6]=6
(4^n+5^n+6^n)^1/n ≥[6^n]^(1/n)
∴lim(4^n+5^n+6^n)^1/n ≥lim[6^n]^(1/n)=6
∴由夹逼定理可知lim(4^n+5^n+6^n)^1/n=6