Hi, can someone help me prove this inequality by Induction
The inequality is: n! ≥ 2^{n-1 }for all natural numbers n
Thank You
1) Define the statement that you'll prove by induction holds for every n:
2) Show Statement(1) is true.
3) ASSUME Statement(k) is true for some k >=1. From that algebracially manipulate it so that you can show that Statment(k+1) must also be true.
It should look like this:
4) 1-3 completes the proof by induction:
You've shown Statement(1) is true by #2,
and, by #3, you've shown that if Statement(k) is true, then Statement(k+1) is true.
Therefore, you've proven Statement(n) is true for all n>=1.