Question

设等比数列{an}的公比q=1/2,前n项和为Sn,则S4/a4=

Answer 1

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