00:01
Okay, so improving by induction, our first step is going to be improved the base case of n equals 1.
00:09
So in the left -hand side, our 2n minus 1, is just going to be 1, and that's going to be equal to 1 squared, which pretty simple is just 1 equals 1, so our base case is correct.
00:31
Now for our inductive, we know at n equal k, and now we're trying to prove it for the n -equal -k, is equal to k plus 1 step.
00:42
So we have 1 plus 3 plus step that dot all the way to 2 k minus 1, and that's going to be equal to k squared.
01:04
To prove the inductive case, we just, we need to make our left -hand side of the equation look like our right -hand side of the equation.
01:16
Or excuse me, we need to make our left -hand side be the k -plus -1 case.
01:22
So we have 1 plus 3, dot, dot, dot, plus 2k minus 1...