1.求Sn=2/2+3/2∧2+4/2∧3+...+n/2∧n-1+n+1/2∧n

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/05/02 02:35:54

1.求Sn=2/2+3/2∧2+4/2∧3+...+n/2∧n-1+n+1/2∧n
2.求数列1,3+5,7+9+11,13+15+17+19,.的前N项和.

1.Sn/2=2/2^2+3/2^3+...+(n+1)/2^(n+1)
=3/2∧2+4/2∧3+...+n/2∧n-1+n+2/2∧(n+1)-[1/2^2+1/2^3+1/2^4+...+1/2^(n+1)]
=S(n+1)-2/2-[1/2-1/2^(n+1)]
=Sn+(n+2)/2^(n+1)-3/2+1/2^(n+1)
=Sn+(n+3)/2^(n+1)-3/2
因此Sn/2=3/2-(n+3)/2^(n+1)
Sn=3-(n+3)/2^n
2.前n项包括的奇数的个数为：1+2+3+...+n=n(n+1)/2
因为前n个奇数之和是n^2,所以数列1,3+5,7+9+11,13+15+17+19,.的前N项和为：
[n(n+1)/2]^2=n^2(n+1)^2/4

已知Sn=2+5n+8n^2+…+(3n-1)n^n-1(n∈N*)求Sn 已知an=(2n+1)*3^n,求Sn Sn=n(n+2)(n+4)的分项等于1/6[n(n+2)(n+4)(n+5)-(n-1)n(n+2)(n+4)]吗? 已知an=5n(n+1)(n+2)(n+3),求数列{an}的前n项和Sn 1+2+3+4+.+n,求Sn 证明不等式：(1/n)^n+(2/n)^n+(3/n)^n+.+(n/n)^n 数列求和：Sn=1/1*2*3+1/2*3*4+.+1/n*(n+1)*(n+2) 求Sn 已知数列{an}的前n项和为Sn=1+2+3+4+…+n,求f(n)= Sn /(n+32)Sn+1的最大值求和：Sn=1*n+2*(n-1)+3*(n-2)+……+n*1 求数列4,9,16,.,3n-1+2^n,.前n项的和Sn 求极限：lim((2n∧2-3n+1)/n+1)×sin n趋于无穷求Sn=C(n,1)+2C(n,2)+...+nC(n,n)