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
问题描述:
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
答
(1)应该是数列{an + 1} 证:a(n+1)=2an+1a(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^nan=2^n-1n=1代入a1=2-1=1,同样满足.数列{an}的通项公式为an=2^...