00:01
Okay, so for this one, we are looking at this even sequence, 2 plus 4 plus 6 plus whatever, right, all the way until n.
00:14
We'll get n times n plus 1.
00:16
All right.
00:17
So for solving by induction, we first are assuming this works for 1.
00:23
So let's just try.
00:24
If we put a 1 in here, does this work? and it sure does right one times two equals two okay so p of one works out now we we want to check does this work for p of k plus one induction is like inducing the next step so so really what we're saying would look like this if we have two plus four plus six plus k we always use k when we're checking these and then does it also work for k plus one so it look kind of like 2k, right, where we've changed the n for a k.
01:03
And then does it work for the next step also? okay.
01:08
And then, so if we're following our rules here, that means that k plus one will replace n, right? that's the step that we're looking at now.
01:21
So we'll just rewrite it like that, put k plus one in brackets, just to be clear.
01:27
Here we've got n.
01:29
That's our end.
01:29
That's our end...