To solve the inequality $n! \geq 2^n - 1$, let's analyze it step by step for different values of $n$, starting from small numbers, and then find a general conclusion.

Step-by-step approach:

1. For $n = 1$: $1! = 1 \quad \text{and} \quad 2^1 - 1 = 1$ So, $1! \geq 2^1 - 1$, which is true.

2. For $n = 2$: $2! = 2 \quad \text{and} \quad 2^2 - 1 = 3$