Question

{an}等比前N项和为Sn,若S3分之S6等于4,求S6分之S12

Answer 1

设公比为q

已知S6/S3=[a1*(q^6-1)/(q-1)]/[a1*(q^3-1)/(q-1)]

=(q^3+1)(q^3-1)/(q^3-1)

=q^3+1=4

q^3=3

所以S12/S6=[a1*(q^12-1)/(q-1)]/[a1*(q^6-1)/(q-1)]

=(q^6+1)(q^6-1)/(q^6-1)

=q^6+1

=(q^3)²+1

=3²+1

=10