lim(1 +2 +…… +n)^1/2-(1 +2+ ..+ (n-1))^1/2答案是2分之根二求过程

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? 若lim(1+2+…+n)/n^2, lim(1/n^2+4/n^2+7/n^2+…+3n-1/n^2) lim(n→∞)(sin(n+√(n^2+n)))^2lim(n→∞)(1/n!(1!+2!+…+n!)) lim (1+2+……n）/（n+2）-n/2 n→无限 求当n→∞,Lim(1+2+3+4+……+(n-1)+n)/n lim(1/n+1 +1/n+2 +…+1/n+n) lim(1-1/n)^(n^2)=? lim(1-1/n^2)^n=? lim{[n*(n+1)*……*(2n-1)]^1/n}/n n->无穷答案是4/e lim(n→∞) (1/n)[sin(π/n)+sin(2π/n)+…+sin(nπ/n)]=? 求lim[1-2+3-4……+(2n-1)-2n]/2n-1 计算lim（1/n^2+1+2/n^2+1+…+2k/n^2+1) 求极限lim(n/(n2+1)+n/(n2+2^2)+……+n/(n2+n2)) 求lim(1+√2+……+√n)/n√n lim[1+3+5+…+(2n-1)/[n(2n-1)]等于多少? 求lim n→∞ 1+2+…+n/2n+1的极限 lim(x→∞）1+2+3+…+n/(n+2)(n+4)=?