What is proper way to prove $2^n + 3 \ge n^2$, for all integer $n$ greater than $0$ , using mathematical induction? This is what I had tried:
- $n = 1; 1 + 3 \geq 1; 4 \geq 1$ OK
- Precondition $n = k; 2^{(k + 1)} + 3 \geq (k + 1)^2$
$2 \times 2 ^ k + 3 \geq k^2 + 2k + 1$
but nothing comes out of it. Thank You in advance