Question

已知f（x）=1/x,数列{An}{Bn}满足A1=1,B1=1,且对任意n为正整数,均有An+1=[An×f（An）]

Answer 1

a(n+1)=1 /(1/an+2)

1/an+1=1/an+2

{1/an}等差数列 首项1/a1=1

1/an=1+2(n-1)=2n-1

an=1/2n-1

bn+1-bn=2n-1

bn-bn-1=2(n-1)-1

.

b2-b1=2(2-1)-1

求和

bn-b1=2 (n(n-1))/2-n+1

bn=n^2-2n+1