Question

一个极限问题lim（n趋向于无穷大）n[ln（n+1）－ln(n)],我算的答案是0,书上给的答案是1,那n趋向无穷大,

Answer 1

n[ln（n+1）－ln(n)]=nln((n+1)/n)=nln(1+1/n)=ln(1+1/n)^n

n->无穷大,(1+1/n)^n->e,

lne=1