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 need to check if n is equal to 1 is true.
00:10
Where we get 2 to the power of 1 minus 1, which is equal to 2 to the power of 0, and that's equal to 1.
00:16
Is that the same as 2 to the power of 1 minus 1? or that's equal to 2 minus 1, which is equal to 1.
00:26
So we see that 1 is equal to 1, so the statement holds.
00:29
And now let's move on to condition 2.
00:32
So for condition 2, we assume that n is equal to k is true.
00:37
So let's write that out.
00:40
So we have to k minus 1 is equal to 2k minus 1.
00:45
This is true.
00:47
And now we want to show that n is equal to k plus 1 is true...