00:01
Okay, so what we have is mathematical induction.
00:09
And with mathematical induction, you have to start with the base case.
00:15
So is it true for n equals 1? so what you have to do is, so that a lot of people will just write down 2, but what you're doing is you're plugging in this 1 in for this n, and 2 times 1 is 2, and you're also plugging the 1 in for these two n's.
00:32
So that's 1 times 1 plus 1, which we know 1 plus 1 is 2, times one is also two.
00:39
So is this true? really is your question mark.
00:43
Two equals two is true.
00:46
So now we have to do the inductive step.
00:54
And that is basically n equals k plus one.
00:59
And so what people will do is they'll write down what we started with.
01:02
Let me go back to black.
01:04
I think it's helpful, this is my opinion, to write down the same thing except maybe replace the ends with k's but then you have to replace the end with k plus 1 and what we already know by the base case is that this statement is already true because it was true for the very first one but i use k's instead of ends so it's k, k plus 1.
01:35
Yeah, k, k plus 1, plus 2, k plus 1...