已知数列{an}中,a0=1,a1=2,an+1-3an+2an-1=0,求an
问题描述：
已知数列{an}中,a0=1,a1=2,an+1-3an+2an-1=0,求an
答
a(n+1)-an=2an-2a(n-1)=2[an-a(n-1)][a(n+1)-an]/[an-a(n-1)]=2所以an-a(n-1)是等比数列,q=2所以an-a(n-1)=(a1-a0)*2^(n-1)所以an-a(n-1)=2^(n-1)a(n-1)-a(n-2)=2^(n-2)……a1-a0=2^0相加an-a0=2^(n-1)+……+2^0=2^0...