已知等比数列{an}的前n项和为Sn,且a1=1,a(n+1)=2Sn 设bn=nan,求数列{bn}的前n项和Tn
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/25 12:08:01
已知等比数列{an}的前n项和为Sn,且a1=1,a(n+1)=2Sn 设bn=nan,求数列{bn}的前n项和Tn
![已知等比数列{an}的前n项和为Sn,且a1=1,a(n+1)=2Sn 设bn=nan,求数列{bn}的前n项和Tn](/uploads/image/z/15929001-9-1.jpg?t=%E5%B7%B2%E7%9F%A5%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E4%B8%94a1%3D1%2Ca%28n%2B1%29%3D2Sn+%E8%AE%BEbn%3Dnan%2C%E6%B1%82%E6%95%B0%E5%88%97%7Bbn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CTn)
(1)a(n+1)=2Sn
an=2S(n-1)
两式相减a(n+1)-an=2an
a(n+1)=3an,a(n+1)/an=3,所以an=3^(n-1)
(2)bn=n*3^(n-1)
对于这种等差数列乘以等比数列的求和,一般用错位相减法,过程较多,就不写了
an=2S(n-1)
两式相减a(n+1)-an=2an
a(n+1)=3an,a(n+1)/an=3,所以an=3^(n-1)
(2)bn=n*3^(n-1)
对于这种等差数列乘以等比数列的求和,一般用错位相减法,过程较多,就不写了
已知等比数列{an}的前n项和为Sn=a*2^n+b,且a1=3.设bn=n/an,求数列{bn}的前n项和Tn
已知数列{an}的前N项和为Sn 且an+1=Sn-n+3,a1=2,设Bn=n/Sn-n+2前N项和为Tn 求证Tn
已知数列{an}的前n项和为Sn,a1=1,a(n+1)=1+2Sn.设bn=n/an,求证:数列{bn}的前n项和Tn
已知数列{an}的通项公式为an=2^(2n-1)且bn=nan、求数列{bn}的前n项和Sn
设数列{an}的前n项和为Sn,数列{bn}满足:bn=nan,且数列{bn}的前n项和为(n-1)Sn+2n
已知数列an的前n项和为sn,a1=2,nan+1=sn+n(n+1),设bn=sn/2n,bn小于等于t,
已知数列{an}的前n项和为Sn,且对任意n属于N+有an+Sn=n,设Cn=n(1-bn)求数列{Cn}的前n项和Tn
已知数列{an}的前n项和为Tn,且满足Tn=1-an,数列{bn}的前n项和Sn,Sn=1-bn,设Cn=1/Tn,证
设数列{an}的前n项和为Sn,已知a1=a,an+1=Sn+3^n,n∈N+.设bn=Sn+3n,求数列{bn}的通项
设数列{an}的前n项和为sn,已知a1=a,an+1=sn+3^n,n∈N* (1)设bn=sn-3^n,求数列{bn
设等比数列{an}的前n项和为Sn 等比数列{bn}的前n项和Tn 已知数列{bn}的公比q>0 a1=b1=1 S5=
设数列{an}的前n项和为sn.已知a1=a,an+1=sn-3n,n∈N*,设bn=sn-3n,且bn≠0