等差数列{an}首项为5,公差为d,d>0,bn=1/anan+2,求b前n项和

Question

等差数列{an}首项为5,公差为d,d>0,bn=1/anan+2,求b前n项和

Answer 1

bn=1/[an*(an+2d)] bn*2d=2d/[an*(an+2d)]=(an+2d-an)/[an*(an+2d)]=1/an-1/(an+2d)=1/an-1/an+2 bn=1/2d*(1/an-1/an+2) bn前n项和=1/2d*（1/a1+1/a2-1/an+1-1/an+2）