已知数列{an}满足a1=1,a(n+1)=2an+1.求证(1)数列a(n+1)是等比数列;(2)求an
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已知数列{an}满足a1=1,a(n+1)=2an+1.求证(1)数列a(n+1)是等比数列;(2)求an
已知数列{an}满足a1=1,a(n+1)=2an+1.求证(1)数列a(n+1)是等比数列;(2)求an
已知数列{an}满足a1=1,a(n+1)=2an+1.求证(1)数列a(n+1)是等比数列;(2)求an
(1)
应该是数列{an + 1}
证:
a(n+1)=2an+1
a(n+1)+1=2an+2
[a(n+1)+1]/(an+1)=2,为定值.
a1+1=1+1=2
数列{an+1}是以2为首项,2为公比的等比数列.
(2)
an+1=2^n
an=2^n-1
n=1代入a1=2-1=1,同样满足.
数列{an}的通项公式为an=2^n-1
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