Question

Prove the statement is true using mathematical induction: 2n-1 ≤ n! Use the space below to write your answer. To make the < symbol, you might want to use the < with the underline feature.

Answer 1

Explanation:

Given that n! = n(n - 1)(n - 2)(n - 3)...2×1

We want to show that 2n - 1 ≤ n!

Since

n! = n(n - 1)(n - 2)(n - 3)...2×1

= n(n - 1)!

n! = n(n - 1)(n - 2)!

n! = (n² - n)(n - 2)!

From here obviously,

n! ≥ n

n! ≥ 2n

And

n! ≥ 2n - 1

Which implies

2n - 1 ≤ n!