求[ n^2(k/n-1/(n+1)-1/(n+2)- .-1/(k+1)] 的极限的值

求lim n→+∞(1/n^k+2/n^k+ +n/n^k)有三种情况, 求极限k^2/(n^3+k^3) n趋于无穷,k=1到n 数论又一题求满足1^n+2^n+.n^n=k!的所有正整数对(n,k) 求极限limn→∞(n^2)*(k/n -1/(n+1)-1/(n+2)...-1/(n+k)K与N无关..K是正整数 求极限lim(n→∞)∑(k=1,n)k/(n^2+n+k)详细过程 (n->00) Lim(n+k)/(n^2+k)(n从1—直加到n) 求limn^2(k/n-1/n+1-1/n+2-…-1/n+k)(其中k为与n无关的正整数)n趋向无穷 求下列极限 lim（n→∞）(1+2+.+n)/n^k k为常数 n(n+1)(n+2)数列求和k∑ n(n+1)(n+2)=k(k+1)(k+2)(k+3)(k+4)/4n=1求证明 求[ n^2(k/n-1/(n+1)-1/(n+2)- .-1/(k+1)] 的极限的值 求证:对任何自然数n,1*2*3...*k+2*3*4...(k+1)+...n(n+1)...(n+k-1)=[n(n+1)...(n+k)]/(k+1) 用定积分求极限lim(n->∞)∑(k=1,n)n/(n^2+k^2) (n+1)(n+2)(n-4)(n-5)+k为完全平方式,求K的值急 求极限 n趋向于无穷大 lim n^2[k/n-1/(n+1)-1/(n+2)-……-1/(n+k)] 数列a[n+1]=k+(2k+1)a[n]+(k(k+1)a[n](a[n+1]))^1/2 已知a1=0 k属于N 求a[n]属于N更正a[n+1]=k+(2k+1)a[n]+2(k(k+1)a[n](a[n]+1))^1/2 数列a[n+1]=k+(2k+1)a[n]+(k(k+1)a[n](a[n+1]))^1/2 已知a1=0 k属于N 求a[n]属于N更正a[n+1]=k+(2k+1)a[n]+2(k(k+1)a[n](a[n]+1))^1/2 数列极限 lim[kn^2/n-n^2/(n+1)-n^2/(n+2)-...-n^2/(n+k)] lim(n趋于无穷)[Σ(k从1到n)ln(1+k/n)/(n+k/n)]答案是2ln2-1,求过程