设等比数列{an}的公比q=1/2,前n项和为Sn,则S4/a4=

设等比数列{an}的公比q=1/2,前n项和为Sn,则S4/a4=
设等比数列{an}的公比q=1/2,前n项和为Sn,则S4/a4=

设等比数列{an}的公比q=1/2,前n项和为Sn,则S4/a4=
s4/a4
=[a1(1-q^4)/(1-q)]/a1q^3
=[(1-q^4)/(1-q)]/q^3
=[(1-q)(1+q)(1+q^2)]/(1-q)]/q^3
=(1+q)(1+q^2)/q^3
=(1+1/2)*(1+1/2^2)/(1/2)^3
=(3/2*5/4)/(1/8)
=15/8*8
=15

解:S4=a1(1-1/(2^4)/(1-1/2)=15a1/8
a4=a1/8
S4/a4=15

15

S4/a4=[a1(1-q^4)/(1-q)]/a1q3=(1-q^4)/(1-q)q^3=15