00:01
Hi, in the given problem we will be proving n factorial is greater than 2 to the power n for n greater or equal to 4 using mathematical induction.
00:15
So, mathematical induction is the best method in this case.
00:20
So, we will start with n is equal to 4.
00:23
So, at n is equal to 4, we have 4 factorial.
00:28
So, this is equal to 24.
00:34
Now, this 2 to the power n would be equal to 2 to the power 4.
00:41
So, that is equal to 32.
00:47
So, 16, this is 16.
00:52
So, therefore, we can see that 24 is greater than 16, which means this is verified for n is equal to 4.
00:59
Now, we will assume that this is true for n factorial is true for n is equal to k or we can say this is for n is equal to k, this is true.
01:12
So, k factorial is greater than 2 to the power k.
01:15
Now take n is equal to k plus 1...