00:01
Okay, so we want to use mathematical induction to show that the following is true.
00:05
Well, we need to start with condition 1.
00:08
That is, we need to show that n is equal to 1 is true.
00:11
So we get 1 squared plus 1, but that's equal to 2, and 2 is divisible by 2.
00:17
So this is true.
00:18
And then for condition 2, we want to assume that n squared plus n, when n is equal to k, this is true.
00:30
So that means k squared plus k is divisible by 2.
00:39
And now we want to show that n is equal to k plus 1 is also divisible by 2.
00:46
So let's see.
00:49
We would have k plus 1 to the power of 2 plus k plus 1.
00:57
Well, let's factor out a k plus 1.
01:01
And then we have a k plus 1 times a k plus 1 plus 1, and that's equal to k plus 2 times k plus 2.
01:17
So let's expand this.
01:19
So we get k squared plus 4k and then plus.
01:33
Okay, so let's rewrite this as k squared plus a k and then plus 3k plus a 4...