Question

n趋近于无穷大,求(1+2^n)^(1/n)的极限

Answer 1

lim(n→∞) (1+2^n)^(1/n)

=lim(n→∞) e^{ln[(1+2^n)^(1/n)]}

=lim(n→∞) e^[ln(1+2^n)/n]

=e^ lim(n→∞) [ln(1+2^n)/n]

=e^ lim(n→∞) [(2^n)*ln2/(1+2^n)]

=e^(ln2)=2