数列{an}的前n项和为Sn,若an=5Sn-3(n∈N*),求lim[a1+a3+a5+…+a(2n+1)]的值_数学解答

数列{an}的前n项和为Sn,若an=5Sn-3(n∈N*),求lim[a1+a3+a5+…+a(2n+1)]的值

人气：383 ℃　时间：2020-01-30 14:16:17

解答

a1=5sn-3 = 5a1 -3
a1=3/4
an-an-1 = 5sn-3 -(5sn-1 -3)=5(sn-sn-1)=5an
an= -1/4*an-1
an+2 = 1/16*an
[a1+a3+a5+…+a(2n+1)] = [3/4 - 3/4*1/16^n]/[1-1/16] =
lim[a1+a3+a5+…+a(2n+1)]
=lim[3/4 - 3/4*1/16^n]/[1-1/16]
= 4/5