当n趋于无穷大时,n次根号下n是否等于1?

lim_(n->infinity) n^(1/n) = 1
Steps:
lim_(n->infinity) n^(1/n)
= e^(lim_(n->infinity) (log(n))/n)
Using L'Hospital's rule:
lim_(n->infinity) (log(n))/n
= lim_(n->infinity) (( dlog(n))/( dn))/(( dn)/( dn));
lim_(n->infinity) n^(1/n)
= e^(lim_(n->infinity) 1/n)
= e^(1/(lim_(n->infinity) n))
= e^0
= 1

求极限的话，应该是1