在等比数列｛an｝中,若S6/S3=3,求S9/S6
问题描述：
在等比数列｛an｝中,若S6/S3=3,求S9/S6
答
S6/S3=[a1(q^6 -1)/(q-1)]/[a1(q^3 -1)/(q-1)]=q^3 +1=3
S9/S6=[a1(q^9 -1)/(q-1)]/[a1(q^6 -1)/(q-1)]
=(q^9-1)/(q^6 -1)
=[(q^3 -1)(q^6+q^3+1)]/[(q^3+1)(q^3 -1)]
=(q^6 +q^3 +1)/(q^3 +1)
=[(q^3+1)^2 -q^3]/(q^3+1)
=[(q^3+1)^2 -(q^3+1)+1]/(q^3+1)
=(9-3+1)/3
=7/3