求当n趋近于无穷时,n[ln(n-1)-lnn]的极限

Question

求当n趋近于无穷时,n[ln(n-1)-lnn]的极限

Answer 1

n→∞,lim n[ln(n-1)-lnn]=lim n*[ln(n-1/n)]=lim [ln(1-1/n)^n]因为函数f(x)=ln x 连续,所以归结得：lim [ln(1-1/n)^n]=ln [lim(1+1/-n)^n]而：lim(1+1/-n)^n=lim(1+1/-n)^-(-n)=e^-1故：原式=ln e^-1=-1即：n→∞,...