If `P(n)` is the statement `2^ngeq3n ,` and if `P(r)` is true, prove that `P(r+1)` is true.

Explanation

To prove that if \( P(r) \) is true, then \( P(r+1) \) is also true for the statement \( P(n) : 2^n \geq 3n \), we will follow the principle of mathematical induction.

### Step 1: Base Case
First, we need to establish the base case. We will check if \( P(1) \) holds true.

\[ P(1): 2^1 \geq 3 \cdot 1 \]
...