在等比数列{an}中,若S6/S3=3,求S9/S6
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在等比数列{an}中,若S6/S3=3,求S9/S6
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
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
等比数列 S6/S3=3 则S9/S6=?
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