Proof by Induction - Example 3

[LizardanNet]

Thanks!, Discrete Math Test in 2 hours!! ... Last exam to Graduate!

[sheanemmanuelporcia]

Omg you just saved me before the day on my exam. thank you so much!!!

[patrickjmt]

awesome, the comment i read just before this was someone promising to make me a pie. maybe we can all get together on the same night.

[sofiagarcia]

Whenever I freak out and don't understand something, even after asking for help/getting extra review, I always come to your channel and you clear everything up! Thank you!

[extremeloco]

For anyone confused about the left side becoming 2^k+1 - 1 / 2^k+1, what happened was : when he multiplied both sidees by 2. it was multiplied by 2^1, so when 2^1 x 2^k, that becomes 2^k+1

2^k+1 - 2

2^k+1

[truepersian]

I used to hate proofs...but now I feel like I can tackle most of em without a problem *knock on wood*

[patrickjmt]

@SpiritualAtheist no, the argument is not circular at all. it is certainly logical to do this

[patrickjmt]

@flopski of course : ) try to prove 1+ 2 + 3 + dot dot dot + n = 10^n
it will be hard to justify this though : )

[patrickjmt]

@valerine11 i have about a playlist with about 200 videos on my channel

[patrickjmt]

@EdMahoney19 your very first sentence does not make sense to me.

[patrickjmt]

@TheConstipatedcamel you just assume it is true, that is the magic of induction.

[patrickjmt]

@MonoMilitiaMusic you are going to change your major because of one class?

[patrickjmt]

@MonoMilitiaMusic hope it turns out ok for you

[SneakyMrSnake]

Wow this is a lot easier than what they try to teach in school

[oldmpsProductions]

you. are. the. best. seriously when i get my engineering degree(s) i'll make sure they give me two and i'll mail you one. you teach better in a video than my useless professors can teach in person. one of your 5-8 minute videos clears up all the junk they've been attempting to explain over the past few weeks. you are a man of men and i hope you get everything you want out of life.

[mulimotola]

How do you know when to work with the whole equation that needs to be proved (like in the previous examples) or just with the left side like in this example? What is the reasoning behind it? Thanks

[SpiritualAtheist]

In your induction step aren't you just assuming to be true that which you set out to prove? You just replace n with k, which you define as being equal? It seems that you have proved the statement to be true by assuming it to be true. I'm not saying that the math doesn't work out, but it's all just begging the question (ie, circular), isn't it?

[aahmadiii]

Why..you need to explain what you are doing...like...you said you were going to solve the left hand side, then you solved the right hand side and that was its RHS=RHS 

[saadafm]

Good Lord THANK YOU. At 2:40 I was stuck on how to find common denominators but I forget that multiplying 2^k by 2 just results in 2^(k+1). It's the simplest things I always forget. Thank you sir.

[museethio]

I admire your mathematical art patrick. I am in calculus one and I wish I can solve all the problems easily like you do.