Solution to By using mathematical induction prove that (n+1)! > 2^(n+1) for n, where n is a … - Sikademy
Author Image

Archangel Macsika

By using mathematical induction prove that (n+1)! > 2^(n+1) for n, where n is a positive integer greater than or equal to 4

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

Prove (n+1)! > 2^{(n+1)} :


Base case: n = 4

(4+1)! = 5! = 120 > 2^{(4+1)} = 2^5 = 32 -> true


suppose for some n: n! > 2^n , let's prove that (n+1)! > 2^{(n+1)}

(n+1)! = n! * (n+1)

2^{(n+1)} = 2 * 2^n

using assumption that n! > 2^n it is obvious that n! * (n+1) > 2 * 2^n , since n+1 > 2 for n \ge 4 .

Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-3388-qpid-2087