lim(1/n^3+(1+2)/n^3+...+(1+2+...+n)/n^3)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/06 18:01:44
lim(1/n^3+(1+2)/n^3+...+(1+2+...+n)/n^3)
n趋于无穷
n趋于无穷
令S(n)=1+(1+2)+(1+2+3)+...+(1+2+...+n)
设an = 1+2+...+n = n(n+1)/2
则
Sn = a1 + a2 + ...+ an
= 1(1+1)/2 + 2(2+1)/2 + ...+ n(n+1)/2
= [1(1+1) + 2(2+1) + ...+ n(n+1)]/2
= [(1*1 + 2*2 + ...+ n*n) + (1 + 2 + ...+ n)]/2
= [bn + an]/2
其中bn = 1*1 + 2*2 + ...+ n*n
= n(n+1)(2n+1)/6
故
Sn = [bn + an]/2
= [n(n+1)(2n+1)/6 + n(n+1)/2]/2
lim(1/n^3+(1+2)/n^3+...+(1+2+...+n)/n^3)=1/6
设an = 1+2+...+n = n(n+1)/2
则
Sn = a1 + a2 + ...+ an
= 1(1+1)/2 + 2(2+1)/2 + ...+ n(n+1)/2
= [1(1+1) + 2(2+1) + ...+ n(n+1)]/2
= [(1*1 + 2*2 + ...+ n*n) + (1 + 2 + ...+ n)]/2
= [bn + an]/2
其中bn = 1*1 + 2*2 + ...+ n*n
= n(n+1)(2n+1)/6
故
Sn = [bn + an]/2
= [n(n+1)(2n+1)/6 + n(n+1)/2]/2
lim(1/n^3+(1+2)/n^3+...+(1+2+...+n)/n^3)=1/6
lim[(n+3)/(n+1))]^(n-2) 【n无穷大】
lim n->无穷大(2^n-1)/(3^n+1)
lim根号n^2+n+1/3n-2
lim(3^2n+5^n)/(1+9^n)
求lim n→∞ (1+2/n)^n+3
lim(n→∞)[1/(3n+1)+1/(3n+2)+~1/(3n+n)]
求极限lim [ 2^(n+1)+3^(n+1)]/2^n+3^n (n→∞)
lim n趋于无穷大(1/n^2+3/n^2+.+2n-1/n^2
lim(1/n^2+4/n^2+7/n^2+…+3n-1/n^2)
求极限 lim(n->无穷)[(3n^2-2)/(3n^2+4)]^[n(n+1)]
求lim(n+1)(n+2)(n+3)/(n^4+n^2+1)
lim n →∞ (1^n+3^n+2^n)^1/n,求数列极限