已知数列{an}中,a1=1,a2=5/3,a(n+2)=5/3a(n+1)-2/3an,求数列{an}
问题描述:
已知数列{an}中,a1=1,a2=5/3,a(n+2)=5/3a(n+1)-2/3an,求数列{an}
答
由 a(n+2) = 5/3a(n+1) - 2/3an可得,a(n+2) - a(n+1) = 2/3[a(n+1)-an][a(n+2)-a(n+1)] / [a(n+1)-an] = 2/3设 [a(n+1)-an] = bn则 b(n+1)/bn = 2/3b1 = a2 - a1 = 2/3所以,bn = 2/3 *(2/3)^(n-1) = (2/3)^n所以,a(n...