lim(n->∞){1/2*4+1/3*5+...+1/(n+1)(n+3)=?

lim(n+3)(4-n)/(n-1)(3-2n) lim(n^3+n)/(n^4-3n^2+1) 一道极限题,lim[n^2(2n+1)]/(n^3+n+4)n->∞ 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 求lim n→∞ (1+2/n)^n+3 lim(n→∞)[1-(2n/n+3)] lim(n→∞)(2n-1/n+3) 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->∞)[2^(2n-1)+1]/(4^n-3^n)=? 求当n→∞,Lim(1+2+3+4+……+(n-1)+n)/n lim (n!+(n-1)!+(n-2)!+(N-3)!+⋯..+2!+1)/n!其中n→∞ 求极限,lim(x->0) (1-2sinx)^(3/x)lim(n->+∞) (n!-4^n) / (6+ln(n)+n^2) 计算下列极限：1）lim(n→∞) 1/n3 2）lim(n→∞)4n+1/3n-11）lim(n→∞) 1/n3 2）lim(n→∞)4n+1/3n-13) lim(n→∞) (1/3)n4)lim(n→∞)n3+2n-5/5n3-n 5) lim(n→∞)(1+1/2n)n 6) lim(n→∞)2x3-x2+1/3x2+2x-9 7) lim(x→0 )sin3x/sin7x8) lim(n->∞){1/2*4+1/3*5+...+1/(n+1)(n+3)=? lim(n→∞) 2n^2+1/3n^2-4 lim(x→∞）1+2+3+…+n/(n+2)(n+4)=? lim[(n+3)/(n+1))]^(n-2) 【n无穷大】