lim(n→∞)[ln(n+1)]/lnn 这个极限怎么算啊?
问题描述:
lim(n→∞)[ln(n+1)]/lnn 这个极限怎么算啊?
答
lim(n→∞)[ln(n+1)]/lnn =lim(n→∞)[ln(n+1)/n)] =lim(n→∞)[ln(1+1/n)]=0
答
利用洛必达法则
lim【n→∞】[ln(n+1)]/lnn
=lim【n→∞】[1/(n+1)]/(1/n)
=lim【n→∞】n/(n+1)
=1
答案:1