00:01
Okay, so whenever i'm given a equation, and i'm trying to prove if it's true or false, what i could do to prove that it's true is transform my left side until eventually reaches my right side.
00:12
To prove that it's false, i only need to provide one counter example.
00:15
So in this case, i'm going to try to prove that this is true.
00:17
I'm going to look at my left side and try to transform it to 2n.
00:21
Okay, so let's say that this is actually, this is actually the expansion of a binomial with one plus.
00:32
So let's rewrite this, is what i'm going to say.
00:34
So the sum from k equals zero to n, n choose k.
00:39
Let's say my first term is just one to the n minus kth power.
00:43
And the reason we don't have a written here is one to anything is just one.
00:46
And my other term must be positive one as well because we don't have anything written here...