设等比数列{an}的前n项之和为Sn,已知S10⼀S5=2,则S15⼀S5=

2025-06-26 11:57:20
推荐回答(1个)
回答1:

q≠1,
不然的话,
s10:s5=2:1≠1:2.
s10=a1(1-q^10)/(1-q),
s5=
a1(1-q^5)/(1-q),
s10:s5=1+q^5=1/2,
q^5=-1/2.
s15:s5
=1+q^5+q^10=1-1/2+1/4
=3/4.
(注:1-q^15=1-(q^5)^3,用立方差公式分解)
满意谢谢及时采纳,并点好评哦~~