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等比数列{an}的前n项和为Sn,若s4/s2=3,s6/s4=?
题目详情
等比数列{an}的前n项和为Sn,若s4/s2=3,s6/s4=?
▼优质解答
答案和解析
s4=a1+a2+a3+a4=a1(1+q+q^2+q^3)
s2=a1+a2=a1(1+q)
s4/s2=(1+q+q^2+q^3)/(1+q)=1+q^2=3 q^2=2
s6/s4=a1(1+q+q2+q3+q4+q5)/a1(1+q+q2+q3)=1+(q4+q5)/(3+q(1+q2))=1+q4(1+q)/(3+3q)=1+q4/3=1+2^2/3=7/3
望采纳祝学习进步
s2=a1+a2=a1(1+q)
s4/s2=(1+q+q^2+q^3)/(1+q)=1+q^2=3 q^2=2
s6/s4=a1(1+q+q2+q3+q4+q5)/a1(1+q+q2+q3)=1+(q4+q5)/(3+q(1+q2))=1+q4(1+q)/(3+3q)=1+q4/3=1+2^2/3=7/3
望采纳祝学习进步
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