Let an=n+ 1.

1) When n= 1, 2, 3, ..., we can know that the general formula is initial (the countability of the formula should not need to be proved);

2) If the general formula is still valid when n=k, then: AK = k+1;

3) When n=k+ 1, the condition is: a (k+1) = AK 2-k * AK+1.

=(k+ 1)^2-k*(k+ 1)+ 1

=k+2

=(k+ 1)+ 1

Therefore, the formula is recursive. So the general formula can be applied to any integer.

That is, the general formula an=n+ 1 is demand.