已知数列{an}为等比数列前n项和为Sn 则Sn,S2n-Sn,S3n-S2n 是等比数列吗？ 写

Question

已知数列{an}为等比数列前n项和为Sn 则Sn,S2n-Sn,S3n-S2n 是等比数列吗？ 写出过程

Answer 1

an = a1.q^(n-1)
Sn = a1(q^n -1)/(q-1)

[S(2n)- Sn]^2
= [a1(q^(2n) -1)/(q-1) - a1(q^n -1)/(q-1)]^2
=[a1/(q-1)]^2 .(q^(2n)- q^n )^2
=[a1/(q-1)]^2 .[q^(4n)-2q^(3n)+ q^(2n) ]

Sn . [S(3n) - S(2n)]
=[a1(q^n -1)/(q-1)] .{ [a1(q^(3n) -q^(2n)] / (q-1) }
=[a1/(q-1)]^2 . [ q^(4n)-2q^(3n) + q^(2n) ]
=[S(2n)- Sn]^2

=>Sn,S(2n)-Sn,S(3n)-S(2n) 成等比数列

Answer 2

按等比定义来，追答

如果你觉得满意的话，请采纳一下或好评，谢谢，

如果你觉得满意的话，请采纳一下或好评，谢谢…

像素不好

像素不好……