Mathematical Induction with Divisibility: 3^(2n + 1) + 2^(n + 2) is Divisible by 7
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- เผยแพร่เมื่อ 10 ก.พ. 2020
- In this video I prove by induction that 3^(2n + 1) + 2^(n + 2) is divisible by 7 for all nonnegative integers n. I hope this video helps:)
Hands down the most clear explanation of divisibility induction I've seen. Genuinely thank you and congratulations every single video of yours on induction I've seen holds up as well
thank you!
Wow I had been stuck on a problem for literally hours. This was the best explanation ive seen. Thank you
You are indeed a Maths sorcerer.
I've tried proving this particular question but it seemed almost impossible till I watched this and saw my mistakes. Thanks a lot.
THANK YOU SIR!
YOU ARE SO KIND SIR, YOU ARE SUCH A BIG MATHEMATICIAN, BUT ALWAYS SO HUMBLE, THANK YOU!
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Thank you!!
I have been looking for so long for this exact kind of question, i messed this up in my exams. Thanks a bunch.
Jeff Bezos before Amazon (without haircut)
Was doing a pastpaper and it had this question, i was so frustrated because i couldn't get the answer and I'd been trying for hours.... until i found this!. You're literally an angel, Thankyou for this! Your method is way easier...the f(k+1) -f(k) got me confused but now i get it
Best explanation ive seen so far ! Thank you 🙏
was struggling on precalc review... thank you this helped so much
Thankyou so much..
Tomorrow is my exam and u helped me a lot..
Idk the result..
But u gained so much respect
Good luck!
Great way of understanding the concept ..
Love from India
You helped me a lot sir, for my exam. 💕 from India :)
Would I be correct if I said that the value of m on the formula b =ma is the base case?
what does claim mean mathematically saying sir, i often heard that word whenever i see someone proving their argument in math also the other words like trivial etc where all of that words came from sir
Here is how to proof 3^(2n + 1) + 2^(n+2) is divisible by 7 w/o induction.
3^(2n+1) + 2^(n+2) =
3*9^n + 4*2^n =
3*(2+7)^n + 4*2^n =
3*2^n + 4*2^n (mod 7) =
7*2^n (mod 7) =
0 (mod 7).
Therefore 3^(2n+1) + 2^(n+2) is divisible by 7.
respect to you sir you always make things clear all the way from Africa
wow that's awesome, Africa so cool! Very happy it helped!!
Samina mina ay ay ।
what if instead it was a greater than or equal to sign instead of a plus sign? Ive been having problems finding examples where the lhs and rhs are both to the power of K
tq for nailing things out, got so much clearer now
Excellent!
The "2 blah + 7 blah is 9 blah" had me rolling.
thank you man, you are a genius
Excellent sir (from India)
you deserve the title math sorcerer
if i got 7(9m+2^k+2) as a proof is it ok ? or it just has one solution ?
Respect to you sir ......u are great helper ..I'm from Pakistan
Thank you !
how would you use proof by induction to prove a function is not divisible by a real number, like n^3 +2 for example is not divisible by 8
Amazing!
Legend!!
When you first learned proof by induction, did it feel like circular reasoning to you?
I actually did not even understand the reasoning behind it. I could write the proofs but didn't understand why induction worked. I remember reading my book over and over. It kept talking about dominoes and I didn't understand. I was able to prove things with it though. The only proofs I really struggled with were the inequality ones, soooo hard for beginners!!
So yes, it felt circular I think. I just remember not understanding why it worked, at all!! I should make a video on that, explaining why it actually works intuitively and mathematically.
@@TheMathSorcerer yes sir, that would be perfect!
I am able to prove using the Induction method, but the problem is, that I do not feel it is rigorous, and I do not understand that why does it always seem to work for k+1
Mark Dave
Yes buddy!
How about for all positive integers n?
2:23 did you mean "when n equals k plus one" and not "k plus two?"
This helped. Thank you.
You a great teacher.
Thank you sir
You are welcome!
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Wow this was so helpful!
👍
Brilliant
awesomeee
Thank you, great explanation
You are welcome!
amazing
Thanks so much!!!
You are welcome!
thank you
beautiful
Thanks sir
What is mean 7m i did not got it
Thanks Man
thank you the math sorcerer!
thank you Alex Reynolds!
@@omeedmehrzad6089 Thank you Kate Mehrzad!
👍
Thx
i love you
Calculus I !!! :)
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love from Pakistan
❤️
Bad teaching
Thx Bro👍
Hey I have a similar problem 7 | 3⌃(4n+1)-5⌃(2n-1). So I end up with way bigger numbers going through the problem, 81 and 25 if you test the problem you'll see what I mean, I don't really know what to do with them, any help would be appreciated!
to further explain he gets 9 and 2 but I get 81 and 25 so it's a bit more complicated
Tnx sir