Question

数列{an}的前项和为Sn=n^2/2-2n,数列{bn}满足bn=(an+1)/an,求数列{bn}中值最大的项和值最

Answer 1

an=Sn-Sn-1=(n^2/2-2n)-((n-1)^2/2-2(n-1))

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

=n^2/2-2n-n^2/2+n-1/2+2n-2

=n-5/2(n>=2)

n=1,a1=S1=1/2-2=-3/2

a1=1-5/2=-3/2

an=n-5/2(n,N*)

bn=(an+1)/an=(n-5/2+1)/(n-5/2)

=(n-3/2)/(n-5/2)

=(n-5/2+1)/(n-5/2)

=1+1/(n-5/2)

n=3,bmax=3

n=2,bmin=1+1/(-1/2)=-1

所以数列bn中值最大的项为3,最小的项为-1