A2=3

A3=7

A4= 15

A5=3 1

Guess an = 2 n- 1

Prove by mathematical induction

When n= 1, A 1= 1 =2- 1 holds.

If n=k, AK = 2 k- 1.

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

N=k+ 1。

An=2^n- 1