已知等差数列{an}的前n项和为Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn已知等差数列{an}的前n项和Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn,试求{bn}的前n项和Tn
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 20:43:43
![已知等差数列{an}的前n项和为Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn已知等差数列{an}的前n项和Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn,试求{bn}的前n项和Tn](/uploads/image/z/1999152-0-2.jpg?t=%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E5%A6%82%E6%9E%9CSn%3D%28an%2B1%2F2%29%5E2%28n%E2%88%88N%2B0%2Cbn%3D%28-1%29%5En%2ASn%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%2C%E5%A6%82%E6%9E%9CSn%3D%28an%2B1%2F2%29%5E2%28n%E2%88%88N%2B0%2Cbn%3D%28-1%29%5En%2ASn%2C%E8%AF%95%E6%B1%82%7Bbn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CTn)
已知等差数列{an}的前n项和为Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn已知等差数列{an}的前n项和Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn,试求{bn}的前n项和Tn
已知等差数列{an}的前n项和为Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn
已知等差数列{an}的前n项和Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn,试求{bn}的前n项和Tn
已知等差数列{an}的前n项和为Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn已知等差数列{an}的前n项和Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn,试求{bn}的前n项和Tn
Sn=((An+1)/2)^2
A1=S1=((A1+1)/2)^2
(A1-1)^2=0
A1=1
Sn=n(A1+An)/2=n(1+An)/2=((An+1)/2)^2
(An+1)/2=n
An=2n-1
Sn=n(1+2n-1)/2=n^2
Bn=(-1)^n×Sn=(-1)^n×Sn^2
如果n为偶数
设C(n/2)=B(n-1)+Bn=-(n-1)^2+n^2=2n-1
Cn=4n-1
Mn是{Cn}前n项和
Mn=(3+4n-1)n/2=n(2n+1)
Tn=M(n/2)=n(n+1)/2
如果n为奇数
C((n+1)/2)=Bn+B(n+1)=-n^2+(n+1)^2=2n+1
Cn=4n-1
Mn=n(2n+1)
Tn=M((n-1)/2)+Bn=(n-1)/2×(2(n-1)/2+1)-n^2=-n(n+1)/2