limn(ln(n加2)减lnn),中间是自然对数,n趋于无穷 求它的极限
问题描述：
limn(ln(n加2)减lnn),中间是自然对数,n趋于无穷 求它的极限
答
lim nln(1 2/n)=lim n*2/n=2
运用等价无穷小ln(1 x)~x (x趋于0)
答
lim n*[ln(n+2)-ln(n)]=lim ln[((n+2)/n)^n]=lim ln (1+(2/n))^n)=ln lim (1+(2/n))^n考虑lim (1+(2/n))^n=lim [(1+(2/n))^(n/2)]^2=[lim (1+(2/n))^(n/2) ]^2根据重要的极限：lim (1+(1/n))^n=e=e^2原极限=ln e^2=2...