So a 1= 1, a2=3, a3=7, a4 =15;

(2) guess? an=2n- 1

Prove: ① It holds when n = 1

(2) Suppose n=k, that is, ak=2k- 1.

Then when n=k+ 1, sk+1= 2ak+1-(k+1), sk = 2ak-k.

The two expressions are subtracted: ak+ 1=2ak+ 1.

From the assumption and the above formula, we can know that AK+ 1 = 2 (2k? 1)+ 1

Namely: AK+ 1 = 2k+ 1? 1

So n=k+ 1 also holds.

From ① ② we know that an=2n- 1, n∈N+ holds.