Question

求极限lim(n→∞)[(1/√n^2+1)+(1/√n^2+1)+….(1/√n^2+n)]

Answer 1

n/√n^2+n<=(1/√n^2+1)+(1/√n^2+1)+….(1/√n^2+n)<=n/√n^2+1
而n/√n^2+n与n/√n^2+1极限均为1
由夹逼准则知
极限为1