00:01
Okay, so we want to use mathematical induction to show that the following is true.
00:06
So let's start with condition one.
00:08
We need to show that n is equal to 1 is true.
00:11
So this gives us 3 to the power of 1 minus 1, which is equal to 3 to the power of 0.
00:17
Well, we need this to be equal to, or this is equal to 1.
00:21
And now let's check if this is equal to our right hand side.
00:24
That's 1 half, 3 to the power of 1 minus 1.
00:27
So we get 2 over 2, which is equal to 1.
00:29
So 1 is the statement.
00:31
Holds and now let's move on to condition two for condition two we assume that n is equal to k is true so let's write out n is equal to k okay okay so this is true and we want to show that n is equal to k plus 1 is true so writing that out we have 1 plus 3 squared all the way up to our k term which is 3k minus 1 as well as our k plus 1 term so that's 3k plus 1 minus 1 so that's k, that should be equal to one -half times three k plus one minus one...