计算lim(1/n2+1+2/n2+1+3/n2+1+...+n/n2+1)

计算lim(1/n2+1+2/n2+1+3/n2+1+...+n/n2+1)
计算lim(1/n2+1+2/n2+1+3/n2+1+...+n/n2+1)

计算lim(1/n2+1+2/n2+1+3/n2+1+...+n/n2+1)
上式=lim(1+2+...+n)/(n^2+1)=lim[n(n+1)/2]/(n^2+1)=1/2 lim[(n^2+n)/(n^2+1)] = 1/2*1 = 1/2,注意到n相对于n^2为低阶.