设数列{an}的前n项和为Sn,a1=1,且数列{Sn}是以2为公比的等比数列.(1)求数列{an}的通项公式(2)求a1+a3+…+a2n-1
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设数列{an}的前n项和为Sn,a1=1,且数列{Sn}是以2为公比的等比数列.(1)求数列{an}的通项公式(2)求a1+a3+…+a2n-1
设数列{an}的前n项和为Sn,a1=1,且数列{Sn}是以2为公比的等比数列.
(1)求数列{an}的通项公式
(2)求a1+a3+…+a2n-1
设数列{an}的前n项和为Sn,a1=1,且数列{Sn}是以2为公比的等比数列.(1)求数列{an}的通项公式(2)求a1+a3+…+a2n-1
1.Sn=2^(n-1)
an=Sn-Sn-1=2^(n-2)
所以n=1 an=1
n>=2 an=2^(n-2)
2.a1+a3+…+a2n-1 =1+2+2^3+2^5+...2^(2n-3)=1+2*(1-4^(n-1))/(1-4)=(2^(2n+1)+1)/3
(1).
Sn=2^(n-1)
an=Sn-Sn-1=2^(n-2)
(a1=1)
(2).
a1+a3+…+a2n-1 =1+2+2^3+2^5+...2^(2n-3)=1+2*(1-4^(n-1))/(1-4)=(2^(2n+1)+1)/3
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