00:01
Okay, so we want to use mathematical induction to show that the following is true.
00:05
So let's start with condition 1.
00:07
So we want to check that and is equal to 1, it's true.
00:11
So let's plug that in.
00:12
So we get 1 times 1 plus 1.
00:15
That's equal to a 2, and now let's check if this is equal to our right hand side.
00:19
So we have 1 over 3 times a 1 times a 1 plus 1, and then a 1 plus 2.
00:25
So we get 2 times a 3, which is 6 over 3.
00:29
So that's equal to 2.
00:31
So we see that this statement is true, or equation is true.
00:35
And now let's see, or let's go on to condition 2.
00:39
So in condition 2, we need to assume that n is equal to k is true.
00:43
So let's write that out as 1 times 2 plus 2 times 3.
00:48
And then we'll add that all the way up to k, and then k plus 1.
00:53
So that's equal to 1 over 3 times k times k plus 1.
00:58
And then k plus 2.
01:01
And then using this, we want to solve or show that n is equal to k plus 1 is true...