This formula for finding the general term is the third method of division:

1, divisible by an;

2. Except the ending term without a, such as constant, (2 n- 1), etc.

3. Except an.a(n+ 1)

This problem is the same as dividing an.a(n+ 1).

Get1/(a (n+1))-1/an = 2,

{1/an} is the arithmetic progression whose first term is 1/a 1= 1 with a tolerance of 2.

1/an = 1+2(n- 1)= 2n- 1

an= 1/(2n- 1)。

After testing, a 1 is also suitable.

After this problem is solved, bn is easy to find and can be obtained in a generation.

bn=2^(n-2)

(2)cn= 1/[n-2+2]= 1/n

1/(cn)^2= 1/n^2< 1/[(n- 1)n]= 1/(n- 1)- 1/n

Tn= 1+ 1/2^2+...+ 1/n^2< 1+[ 1- 1/2+ 1/2- 1/3+...+ 1/(n- 1)- 1/n]

=2- 1/n