Mathematical Induction with Divisibility: 3^(2n + 1) + 2^(n + 2) is Divisible by 7

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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:)

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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

juandirection

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.

extramiletvesonucc.

THANK YOU SIR!

YOU ARE SO KIND SIR, YOU ARE SUCH A BIG MATHEMATICIAN, BUT ALWAYS SO HUMBLE, THANK YOU!
:):):)

johubify

respect to you sir you always make things clear all the way from Africa

fleurysankara

Best explanation ive seen so far ! Thank you 🙏

aldoumene

Great way of understanding the concept ..
Love from India

alokmandal

Respect to you sir are great helper ..I'm from Pakistan

enayahkhan

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

AshleyHan-ui

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

blalalalahd

Would I be correct if I said that the value of m on the formula b =ma is the base case?

Thabang_Kgatla

How about for all positive integers n?

nifahadjiabobakar

2:23 did you mean "when n equals k plus one" and not "k plus two?"

chessandmathguy

Wow I had been stuck on a problem for literally hours. This was the best explanation ive seen. Thank you

zacharyjohn

Thankyou so much..
Tomorrow is my exam and u helped me a lot..
Idk the result..
But u gained so much respect

saumytiwari

Jeff Bezos before Amazon (without haircut)

MdFaizan-thyf

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.

sergeigrigorev

When you first learned proof by induction, did it feel like circular reasoning to you?

markdave

You helped me a lot sir, for my exam. 💕 from India :)

bgaming

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

ELLIPTICALWR

The "2 blah + 7 blah is 9 blah" had me rolling.

leviackerman

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