已知等比数列{an}中,a1+a3=10,a4+a6+5/4,求a4+a6+a8+···+a100
问题描述:
已知等比数列{an}中,a1+a3=10,a4+a6+5/4,求a4+a6+a8+···+a100
答
a1+a3=10 (1)
,a4+a6=5/4 (2)
(2)/(1)=q^3=1/8
q=1/2 a1=8
a4=1
a4+a6+a8+···+a100=1*(1-(1/4)^49)/(1-1/4)=4/3