lim(1/n+2/n+3/n+4/n+5/n+……+n/n)=lim(1/n)+lim(2/n)+……+lim(n/n)成立吗?（n趋近于无穷大）为什么不成立?

lim(n+3)(4-n)/(n-1)(3-2n) lim(n^3+n)/(n^4-3n^2+1) lim[(4+7+...+3n+1)/(n^2-n)]= lim(1/n+2/n+3/n+4/n+5/n+……+n/n)=lim(1/n)+lim(2/n)+……+lim(n/n)成立吗?（n趋近于无穷大）为什么不成立? lim[(n+3)/(n+1))]^(n-2) 【n无穷大】 lim(2^n+3^n)^1 (n趋向无穷) lim n趋向无穷大3n^3+n^2-3/4n^3+2n+1 lim(1/n^2+4/n^2+7/n^2+…+3n-1/n^2) 1、lim n->无穷 根号[(n^4+n+1)-n^2]*(3n+4) 求lim(n+1)(n+2)(n+3)/(n^4+n^2+1) 一道极限题,lim[n^2(2n+1)]/(n^3+n+4)n->∞ lim (n!+(n-1)!+(n-2)!+(N-3)!+⋯..+2!+1)/n!其中n→∞ lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n-1)]求极限 lim（n->无穷大）（1^n+2^n+3^n+4^n）^1/n等于多少 用数列极限证明lim(n→∞)(n^-2)/(n^+n+1)=1中证明如下:lim(n→∞)3n+1/5n-4 高数题：n趋近于0,lim｛1/（n^2+n+1)+2/(n^2+n+2)+3/(n^2+n+3)+.+n/(n^2+n+n)｝=? lim((2n+1)^5(n+10)^3)/((n^2-2n-3)^4)=32 lim(n趋近于无穷)(1+2+3+.+n)/(3n^2+4n)等于多少