假设等比数列{an}的a1=1,S3=7求a1/a2+a2/a3+a3/a4+a4/a5+a5/a6

s3=a1+a2+a3
=a1+a1q+a1q^2
=1+q+q^2
1+q+q^2=7
q^2+q-6=0
(q-2)(q+3)=0
q=2或q=-3
当q=2时
a1/a2+a2/a3+a3/a4+a4/a5+a5/a6
=1/q+1/q+1/q+1/q+1/q
=5/q
=5/2
当q=-3时
a1/a2+a2/a3+a3/a4+a4/a5+a5/a6
=1/q+1/q+1/q+1/q+1/q
=5/q
=-5/3