Trust me guys, he has the best way of presenting the topic!. I've been searching for discrete math vids, and finally found the best one. keep doing what u do✌
i’m a junior in college and you covered this material significantly better and more efficiently than my professor. you have a great way of explaining. keep it up man💪
You prolly dont care but does anybody know of a trick to log back into an Instagram account?? I was stupid forgot my login password. I would love any assistance you can give me
@Kasen Wade I really appreciate your reply. I found the site through google and Im trying it out atm. Looks like it's gonna take a while so I will get back to you later with my results.
I used (7^k = 3 + 4^k) so you end up with 7(7^k)-4(4^k) = 7(3+4^k) - 4(4^k) = 21 + 7(4^k) - 4(4^k) = 21 + 3(4^k) = 3(7+4^k) and since k is a positive integer and the integers are closed under addition and multiplication, 3(7+4^k) = 3z where z is an integer. Bit different but is it still valid?
at 13:56, we we are writing what we want to show, why is the 4k - 3 present in addition to plugging k + 1 into k. if we supposed that n = 1, i understand putting 4k + 3, but if we Want to show P(k + 1), wouldnt we just plug in k + 1 wherever n is present (like we did for the right side)?
Good question. Yes, you can just replace k with k+1 and simplify (I also did this). Writing 1+5+...+(4k+1) is the same as writing 1+5+...+(4k-3)+(4k+1). I just made the term before 4k+1 more explicit because I think it helps us see how we can show what we want to show (by adding (4k+1) to both sides). If you can do without it then it's still perfectly fine.
Maybe someone smarter than me can figure it out. But, to me, it looks like he made a mistake that he mentioned earlier in the video. He manipulated the conclusion and accidentally used the second expanded form from what he wanted and put it back into the proof to get the expression you mentioned. I'm not even sure the end result of the proof even factors nicely, I got 2k^2+3k+1 for the induction step and the expanded form of the right hand side completely and stopped there without factoring back into 2(k+1)^2-(k+1).
