(2) conjecture: an=2/(n+3)

(3) ① When n= 1, a1= 2/(1+3) =1/2, and the equation holds.

(2) Assuming that it holds when n=k, that is, ak=2/(k+3), then when n=k+ 1,

A(k+ 1) (note: the right subscript in brackets) = 2ak/(AK+2) = 2 * (2/k+3)/[2/(k+3)+2] (that is, ak=2/(k+3) is taken to the right of the equation).

③ Verify the equation with ① and ②.