### Home > PC > Chapter 8 > Lesson 8.2.6 > Problem 8-152

8-152.

4! = 24 > 2^{4} = 16 whereas 3! = 6 ≯ 2^{3} = 8.

Assume that *k*! > 2* ^{k}* for

*k*≥ 4.

Hence, by mathematical induction we have proven that *n*! > 2* ^{n}* for

*n*≥ 4.

8-152.

4! = 24 > 2^{4} = 16 whereas 3! = 6 ≯ 2^{3} = 8.

Assume that *k*! > 2* ^{k}* for

Hence, by mathematical induction we have proven that *n*! > 2* ^{n}* for