已知数列{a底n}中,a1=a2=1,且an=an-1+an-2(n≥3,n∈n*),设bn=an/(an+1).(1)求证:b已知数列｛a底n｝中,a1=a2=1,且a底n=a底n-1+a底n-2(n≥3,n∈N*),设b底n=a底n/(a底n+1).(1)求证：b底n+1=1/(1+b底n,n∈N*;(2)求出数列｛b底n

Question

已知数列{a底n}中,a1=a2=1,且an=an-1+an-2(n≥3,n∈n*),设bn=an/(an+1).(1)求证:b
已知数列｛a底n｝中,a1=a2=1,且a底n=a底n-1+a底n-2(n≥3,n∈N*),设b底n=a底n/(a底n+1).(1)求证：b底n+1=1/(1+b底n,n∈N*;(2)求出数列｛b底n｝的前5项

Answer 1

1+bn=1+[an/a(n+1)]=[an+a(n+1)]/a(n+1)=a(n+2)/a(n+1)b(n+1)=a(n+1)/a(n+2)所以b(n+1)=1/(1+bn)b1=a2/a1=1所以b2=1/(1+b1)=1/2b3=1/(1+b2)=2/3b4=1/(1+b3)=3/5b5=5/8