Question

已知f(x)=x/1+x,数列｛an｝满足an=f(an-1)(n≥2,n∈N)且a1=1则a10=

Answer 1

An=f(A(n-1))=A(n-1)/(1+A(n-1))=1/[1+1/A(n-1)]

1/An=1+1/A(n-1)

1/An-1/A(n-1)=1

1/A1=1

数列{1/An}是以1为首项,1为公差的等差数列.

1/An=n

An=1/n

A10=1/10