Induction Proofs

I introduce the steps to doing an Induction Proof. I then work through three examples that I hope will help you understand the concept and complete your homework:)
More Induction Proofs:

[Lionfish]

I rediscovered my passion for math a few years ago. Granted, I was always good with numbers, but given that I have always worked on them from the perspective of just abstract numbers, me learning algebra & calculus for the first time for me was very counter intuitive, but very fascinating. Not only did it make me more interested in math again & choose it as my undergraduate major, it has taught me a great lesson in not assuming that what you know is true & to think before you act. Math teaches important critical thinking skills which are sorely needed in this nation .

[jayceinfinitealgharhythmns]

As you know… I've read the comments and the only thing I can add at this point is I think you teach better than anything the best person in the world at their chosen craft could do! I'm doing Discrete Math and I didn't expect to find this here, but when I saw who had a video the first thing that came to my mind was "In about 30 minutes, any variation of this question thrown my way is easily solved." I know you've said it's students like me is why you teach, but it's teachers like you (although I doubt there's another teacher like you anywhere!) that are the reasons I have grown to love learning! We (the collective students who agree) could never thank you enough for all of this!!!!

[profrobbob]

THANK YOU for paying such close attention!!! I will make the correction:) You are the kind of student teachers like, it shows us that you are really paying attention to what we are teaching you, we don't always have enough of those:(

[profrobbob]

Thank you so much for that testimonial!
I'm glad to see you are still watching and benefiting from my lessons...loyal subscribers like you are the ones who keep me growing:D

[profrobbob]

And "THANK YOU" CJ for that glowing review! I hope you enjoy learning from more of my videos and please help support my channel growth by sharing with your friends and classmates…and tell them how important it is to "SUBSCRIBE" to help educational channels to groW!

[profrobbob]

THANKS from Florida for subscribing and watching:) I wrote down the name and will take it to one of our stores and see if they carry it...if so I will have one in your honor!

[profrobbob]

Thank you very much. I am glad to hear you liked my videos:):):) Why can't all books use the same notation?!

[Fuerii]

You do a great job breaking it down. Not sure why this seemed so obscure in class. After seeing it here it is very doable. I appreciate what you're doing here.

[Keltodadubawo]

Once again, THANK YOU. You got me through trig last year, and you're doing it again this year! You are a blessing!

[mustangrida]

Thanks A LOT for your help! you make math more about understanding rather than memorizing. And there is no reason to have confusion about induction after watching this video in full.

[eddiezj]

Out of all the induction videos i've seen this is the only one that actually makes sense 100%.

[HackingDutchman]

The best explanation I could find on youtube. Thanks a lot. My ''reader'' only works with those summation proofs, so I was very glad to finally found someone explain one of those clearly!!

[hanthenah-education]

ProfRobBob we love you a lot, you are our favorite math YouTuber! -HBJ

[oblivionboy]

I just want to say that this made what, for me, is a very difficult concept to understand much more clear. I especially liked the fact that you didn't leave steps out and assume the audience would grasp it as you worked through the problem (this is quite common for people to d) but instead took the time to explain each of the steps each time you walked through a problem. Well done! :-)

[lanreenilo]

The professor is very insightful. This representation of proof righting by mathematical induction provides the whole techniques and involvements for mathematics to be sound.

[georgesadler]

Professor RobBob, thank you for another incredible video/lecture on Induction Proofs. The higher any student goes in Mathematics and the Sciences, writing proofs is the solution to just about every Mathematical problem. The real beginning of proof writing is in Advanced Calculus One and Two. Any student, who fully understand Advanced Calculus really well will cruse in Mathematics and related technical fields.

[profrobbob]

Thank you for your kind thoughts. My examples represent the type of proofs that are in the Precalculus book I teach from. I did notice a couple of months later that another book I have in my room has other type of problems...but I have not worked them out yet. I am currently working on Geometry notes for the current school year that is starting tomorrow for me. So, I am sorry but I really need to focus on that right now:( I hope you find other videos of mine helpful and you great in school.

[carolfisher]

Hi again!! I am in math 301( Writing and Exploration of Mathematical proofs) at SFSU!! Thanks for helping me pass my math classes throughout the last couple of years!! wish me luck on my proofs midterm today! totally didn't understand induction until I watched this!!

[desireiruke]

ProfRobBob....Thanks for this, I'm grateful, because you are a great teacher

[profrobbob]

Thank you for your kind words, but unfortunately I cannot help with strong induction. I forgotten what that is!!! It has been 18 years since I earned my math degree and I have never taught that concept.