Question

一个数列中,a1=2.a2=1 ana(n-1)/a(n-1)-an=ana(n+1)/an-a(n+1) [n≥2]

Answer 1

ana(n-1)/[a(n-1)-an]=ana(n+1)/[an-a(n+1)]

[a(n-1)-an]/[ana(n-1)]=[an-a(n+1)]/[ana(n+1)]

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

数列{1/an}是等差数列.

1/a1=1/2 1/a2=1/1=1

d=1/a2-1/a1=1-1/2=1/2

数列{1/an}是以1/2为首项,1/2为公差的等差数列.

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

an=2/n

a100=2/100=1/50