lim(n→∞) 根号n+2-根号n+1/根号n+1-根号n

问题描述:

lim(n→∞) 根号n+2-根号n+1/根号n+1-根号n

√n+2-√n+1=1/(√n+2+√n+1)
√n+1-√n=1/(√n+1+√n)
所以原式=lim(n→∞) (√n+1+√n)/(√n+2+√n+1)=1