If a and b are positive, use mathematical induction to prove that `((a+b)/(2))^(n) le (a^(n)+b^(n))/(2) AA n in N`

Explanation

To prove the statement \(\left(\frac{a+b}{2}\right)^{n} \leq \frac{a^{n}+b^{n}}{2}\) for all \(n \in \mathbb{N}\) using mathematical induction, we will follow these steps:

### Step 1: Base Case
We start by checking the base case for \(n = 1\).

**LHS**:
\[
\left(\frac{a+b}{2}\right)^{1} = \frac{a+b}{2}
...