Example of Proof By Induction

Precalculus: Prove the following statement by induction: 5 + 8 + 11 + ... + (3n+2) = n(3n+7)/2. We review the method using this special case.

[MathDoctorBob]

@irfaanfr1 You're welcome, and thanks for the comment! - Bob

[MathDoctorBob]

@vforviolin1 Thanks! Induction is needed in the video "Fibonacci Numbers Using Linear Algebra", but I leave it as an exercise. Do you have a specific problem that you want to see? - Bob

[harleenkaur]

You took less than five minutes to help me understand and my teacher couldn't in two hours. You seriously saved my grade, thank you so much!! 

[bitcrusherNOOP]

A nice example Bob, a little fast for me but after pausing it after each step; so I could confirm the algebra, I could get to the next step.

[MathDoctorBob]

You're welcome! Glad to be of help.

[MathDoctorBob]

@barnamah This is the important part. We use the assumption to swap out the sum up to 3n+2 with n(3n+7)/2. At some point, we must use the induction hypothesis for n. Now combine that with 3n+5 to get a single fraction. - Bob

[MathDoctorBob]

@assassin9110 You're welcome! - Bob

[GenialGris]

This really helped me getting those final pieces together! Thank you so much!

[MathDoctorBob]

@neodine Jiu-jitsu, and stick and knife. Believe it or not, there are some really tough math guys out there. - Bob

[amaam]

I just wanted to tell you that your videos are pretty brilliant. :)

[MathDoctorBob]

You're welcome, and thanks for the kind words!

[DoggoWillink]

Wow, do they teach proofs in precalc now? I saw this in a junior level university class for the first time lol.

[mzemura]

Thank you so much!! this just helped me understand proof by induction in such a simple way

[MathDoctorBob]

It depends on the department. I've taught it to magnet school kids in pre-calc, and both with and without to regular students. I first saw it in high school in comp sci classes.

[MathDoctorBob]

@talk2nguyen Thanks! Pacing math is hard, especially if you are checking every step. The pause button is a big help; I wish I had one for real life. - Bob

[neodine]

You look like a krav maga instructor with your baton and stuff. :D Not so typical math teacher!

[DoggoWillink]

Meaning 300 level, Math Reasoning, Math 300. That's the first time I learned real proof methods, induction being one of them.

[MathDoctorBob]

@stidhemw I never claimed to be good at either. :) - Bob

[alullabyofpain]

does it just work with 1 variable? you used a AP (Pa) of n numbers, which the first is 5 (base) and the last is 3n+2, so you have 2 ``hidden`` numbers, but both on base n, would it work if we had 2 unknown bases like n and m ? thxx

[temp___]

Your voice sounds just like Nicholas Cage. Crazy.