Question

a1=0.2,(an-1)/an=2a(n-1)+1/1-2an,求an

Answer 1

n≥2时,

a(n-1)/an=[2a(n-1)+1]/(1-2an)

2ana(n-1)+an=a(n-1)-2ana(n-1)

a(n-1)-an=4ana(n-1)

等式两边同除以ana(n-1)

1/an -1/a(n-1)=4,为定值.

1/a1=1/0.2=5,数列{1/an}是以5为首项,4为公差的等差数列.

1/an=5+4(n-1)=4n+1

an=1/(4n+1)

数列{an}的通项公式为an=1/(4n+1).