Question

1.已知数列{an},a1=2,an=an-1（下标)/1+an-1（下标) (n大于等于2)，求

1.已知数列{an},a1=2,an=an-1（下标)/1+an-1（下标) (n大于等于2)，求an。
2.已知数列{an}满足an+1（下标)=3an+2（n为正整数)，a1=1,求通项公式an.

Answer 1

Answer 2

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

(2)
a(n+1) = 3an +2
a(n+1) + 1 = 3(an + 1)
=> {an +1 } 是等比数列, q=3
an +1 = 3^(n-1) (a1 +1)
=2.3^(n-1)
an = -1 +2.3^(n-1)