(1+2/3n)∧n的极限怎么求

Question

(1+2/3n)∧n的极限怎么求

Answer 1

你知道n→∞时,lim（1+1/n)^n=e,
lim(1+2/3n)∧n=[（1+2/3n）^3n/2]^2/3,令3n/2=t,因为n→∞,则t=3n/2→∞,
原式=lim[（1+1/t)^t]^2/3=e^2/3