** Claim: **

* Proof. * For , on the left we have 1 and on the right we have . Thus, the formula holds for the case .

Assume then that the formula is true for some . Then,

Hence, if the statement is true for , then it is true for . Since we have established that it is true for , we then have that it is true for all

Positive integers do not include zero. Hence, it is incorrect to say when n=0. The integers start at n=1 and the formula is for n=1 then we have 1+\frac{1}\{2}n and that is equal to 2-\frac{1}/{2}, which is equal to \frac{3}/{2}. The rest can be applied as you stated.

I will write it again in latex sorry about that.