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, and we need to show that n is equal to 1 is true.
00:11
So starting with our left hand side, that's 5 minus 1, which is equal to 4.
00:16
That's the same as our right hand side.
00:20
Well, we get 8 over 4, or actually that's 8 over 2, and that's also equal to 4.
00:26
So this is true.
00:28
And now let's move on to condition 2.
00:30
So in condition 2, we assume that n is equal to k is true.
00:35
So let's write out what that is.
00:37
That's 4 plus 3 plus dot dot dot up to 5k minus 1, or 5 minus k, and that's equal to 1 over 2 k times 9 minus k.
00:50
And using this, we want to show that n is equal to k plus 1 is true.
00:55
Assuming that it is true, we would get the full one...