题目

a(n+1)=(-an-2)/(2an+3)如何构造新数列
急用

提问时间：2020-12-26

答案

a(n+1)=(-an-2)/(2an+3)
a(n+1) +1 = (-an-2)/(2an+3) +1
= (an+1)/(2an+3)
1/[a(n+1) +1] = (2an+3)/(an+1)
= 2+1/(an+1)
1/ [a(n+1) +1] - 1/(an+1) = 2
1/(an+1) - 1/(a1+1) = 2(n-1)
1/(an + 1) = 1/(a1+1) + 2(n-1)
an+1 = 1/[1/(a1+1) + 2(n-1)]
an = 1/[1/(a1+1) + 2(n-1)] - 1