Proof by Induction - Example 2

[teezy]

Damn your lefthandedness sir! You block the problem as it progresses but I am a lefty to so I know the struggle lol.

[hartake]

In case it helps others. 3:59 I never knew you could multiply terms independently like 2/2 * 3k-1, as long as they are equivalent to 1. I always thought you'd multiply the whole expression on both sides always. But its allowed as long as the term is equivalent to 1. He multiplied 3k-1 by 2/2, and then he added that with -5k/2, and the. Simplified that to k/2 - 1. That should be allowed because multiplying by 2/2 is multiplying by 1 which is ok

[EmmnauelPeace]

Patrick that is really a good stuff but I recommend that you make more videos on  Computational algorithms complexity and others...Thanks a lot this has been very useful

[Fulcrum]

You teach it so much better than an online textbook. You're a lot of help to people taking Pre-Calc online. Thank you :)

[shootingstar]

Thank you so much! didn't take long at all to explain and you did simple explaining through each step in your process! Thank you :D

[wonchoi]

My math teacher is horrible at teaching, but you taught me this in just few videos, Thanks!

[melovesmusic]

finals are tomorrow and this saved me, thanks so much! 

[ferusinfo]

If I will pass my exam tomorrow, i've owe you one! I could not understand this topic on my studies but now it's like piece of cake. Come to Poland, teach us.

[memento_mori]

@Alex Gold I know you may have figured it out by now, but notice that: 
when you plug in a positive integer(almost always starting with 1) into (3n-4), (ex. 3(1)-4 = -1, and 3(2)-4=2) you get that exact sequence of integers that is on the left of (3n-4), in this case, "-1 + 2 +5 + 8+" and so forth.

So what we want to know is: does this (3n-4) that yielded that sequence of integers equal whats on the right side of the equation?

That's why we focus on (3n-4) instead of the sequence of integers that is produces.

[iamaFuckokaRaver]

thanks so much for the videos you are much better at explaining than my prof.. isn't even comparable thanks!!

[muzion]

I downloaded 1.5 gig worth of videos from a math teacher in Madrid, forgetting I should have just rode with PatrickJMT all along! I won't make that mistake again!

[jjooeeddrruumm]

I don't usually do this, but these videos are very helpful! Thanks

[TheCancanbob]

thank god for this video, my fp1 exam is tomorrow and this has just helped me learn induction

[beastlybee]

AHhhhh You actually found a way to explain discrete mathematics in English!!! Many thanks

[strawberryswirl]

thank you so much!! a couple of your videos and I can understand calculus better than my 3 hour lecture :)

[monicaj]

u are the reason i am not failing math!! thank u (: !!

[stevewest]

Only one thing I would do differently if I were teaching this.... after the base case, give your students another example at n=4. That drives home the point that the SUM of the pattern on left = the formula on the right. For example @n=4 it goes -1+2+5+8 = 4/2[3(4)-5]. Its NOT 3(4)-4 = 4/2 [3(4)-5]
This will help address a common error before it happens!

[WesternEasternTruth]

Not sure if this is true, but when you think about it, you are proving that two numbers right next to each other are both equaling what it says on the other side. It's like your prof is using (k-1) where we are using (k), and your prof is using (k) where we are using (k+1). They are still both right next to eachother, so it doesn't really matter.

[rvbelmontes]

Thank you so much you have helped me trying to even understand this concept and you make it seem so easy now thank you

[CherryPauper]

I think it can be whatever value you want. If it equates, then move on to proof by induction. My answer came 2 months too late but by now you are probably better than me! lol