00:01
So in this question, we just want to prove that n squared plus 1 is greater than or equal to 2 to the n power, when n is a positive integer between 1 and 4.
00:12
And so since we only have to prove this is true for positive integers from n equals 1 to 4, i'm just going to check them one at a time.
00:25
So if i look at n equals 1, i get 1 squared plus 1 is greater than equal to 2 to the 1.
00:35
On the left, 1 squared is 1, plus 1 is 2.
00:40
2 to the 1 is 2, and it's true that 2 is greater than or equal to 2.
00:51
And then i check n equals 2.
00:54
So i plug in.
00:56
On the left, 2 squared plus 1.
01:00
On the right, 2 square.
01:04
On the left, 4 plus 1 is 5.
01:08
That is greater than or equal to 4.
01:11
That's a true statement.
01:16
Now i check n equals 3...