数列{an}中,a1=1,点(an,an+1)在直线y=2x+1上(1)证明{an+1}为等比数列(2)求an
问题描述:
数列{an}中,a1=1,点(an,an+1)在直线y=2x+1上(1)证明{an+1}为等比数列(2)求an
答
点(an,an+1)在直线y=2x+1上即a(n+1)=2an +1a(n+1)+1=2an +2a(n+1)+1=2(an +1)[a(n+1)+1]/(an+1)=2所以{an +1}是以2公比的等比数列an +1=(a1 +1)q^(n-1)an +1=2 * 2^(n-1)an +1= 2^nan=2^n-1