Question

lim(1+2n)1/n,n趋近于无穷大,求此极限.

Answer 1

如果题目没有错

lim (1+2n)*1/n=lim 1/n+ lim 2n/n=0+2=2

或许楼主说的是

lim (1+2n)^(1/n)

那么

lim (1+2n)^(1/n)=e^lim ln(1+2n)/n

洛必达得

lim (1+2n)^(1/n)=e^lim ln(1+2n)/n=e^lim 2/(1+2n)=e^0=1