求极限lim（3n+2/3n-1）∧2n-1n→∞

Question

求极限
lim （3n+2/3n-1）∧2n-1 n→∞

Answer 1

=(1+3/(3n-1))^[(n-1/3)(2n-1)/(n-1/3)]
因为lim(1+1/n)^n n→∞=e
所以(1+3/(3n-1))^(n-1/3)=e
原式=e^[(2n-1)/(n-1/3)]
=e^[2-1/(3n-1)]
=e^2