Question

利用夹逼定理，求数列极限n趋于无穷 lim(1+2∧n+3∧n)∧1╱n

请问此题右边放大如何求解

Answer 1

3^n <1+2^n+3^n < 3^(n+1)
3 <(1+2^n+3^n)^(1/n) < 3^[(n+1)/n]
lim(n->∞) 3^[(n+1)/n] =3
=>lim(n->∞) (1+2^n+3^n)^(1/n) =3

追问

右边放大为什么等于3呢

追答

lim(n->∞) 3^[(n+1)/n]
=3^(lim(n->∞) [(n+1)/n] )
=3^1
=3