Question

数列的求和问题详解答案

已知等比数列的n项和为Sn，若S6/S3=3。求s9/S6=？，求详解答案。谢谢

Answer 1

S6=a1(q^6-1)/(q-1)
S3=a1(q^3-1)/(q-1)
S6/S3=(q^6-1)/(q^3-1)=3
(q^3+1)(q^3-1)/(q^3-1)=3
q^3+1=3
q^3=2

S9=a1(q^9-1)/(q-1)
所以S9/S6=(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)
=(4+2+1)/(2+1)
=7/3

Answer 2

Sn=a1*(1-q^n)/(1-q)
S6/S3=(1-q^6)/(1-q^3)=3
q^3=2
S9/S6=(1-q^9)/(1-q^6)=7/3

Answer 3

Sn=a1*(1-q^n)/(1-q)
S6/S3=(1-q^6)/(1-q^3)=3
q^3=2
S9/S6=(1-q^9)/(1-q^6)=7/3

Answer 4

Sn=a1*(1-q^n)/(1-q)
S6/S3=(1-q^6)/(1-q^3)=3
q^3=2
S9/S6=(1-q^9)/(1-q^6)=7/3

是个好方法！你可以取