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

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  • Опубликовано: 24 дек 2024

Комментарии • 87

  • @juandirection3751
    @juandirection3751 2 года назад +30

    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

  • @Faizanhere_2002
    @Faizanhere_2002 Год назад +3

    Jeff Bezos before Amazon (without haircut)

  • @zacharyjohn329
    @zacharyjohn329 3 года назад +14

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

  • @extramiletvesonucc.2892
    @extramiletvesonucc.2892 3 года назад +6

    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.

  • @whitb62
    @whitb62 20 дней назад

    You are the MVP with math proof content sir, especially mathematical induction. I love it!

  • @johubify
    @johubify 4 года назад +23

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

  • @leviackerman3033
    @leviackerman3033 2 года назад +2

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

  • @sergeigrigorev2180
    @sergeigrigorev2180 3 года назад +2

    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.

  • @saumytiwari7
    @saumytiwari7 3 года назад +9

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

  • @fleurysankara5081
    @fleurysankara5081 4 года назад +7

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

  • @bgaming93
    @bgaming93 Год назад +2

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

  • @alokmandal6353
    @alokmandal6353 Год назад

    Great way of understanding the concept ..
    Love from India

  • @leviackerman3033
    @leviackerman3033 2 года назад

    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

  • @aromaoflifewithromakhare4035
    @aromaoflifewithromakhare4035 2 месяца назад

    I just love the way you teach

  • @LakshayDhaka08
    @LakshayDhaka08 2 года назад

    Excellent sir (from India)

  • @markdave2456
    @markdave2456 4 года назад +5

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

    • @TheMathSorcerer
      @TheMathSorcerer  4 года назад +6

      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!!

    • @TheMathSorcerer
      @TheMathSorcerer  4 года назад +1

      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.

    • @johubify
      @johubify 4 года назад

      @@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

    • @johubify
      @johubify 4 года назад +1

      Mark Dave
      Yes buddy!

  • @aldoumene6201
    @aldoumene6201 3 года назад +1

    Best explanation ive seen so far ! Thank you 🙏

  • @konchu5221
    @konchu5221 Год назад

    was struggling on precalc review... thank you this helped so much

  • @enayahkhan6491
    @enayahkhan6491 4 года назад +1

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

  • @davidfisher9626
    @davidfisher9626 4 года назад

    you deserve the title math sorcerer

  • @ELLIPTICALWR
    @ELLIPTICALWR Год назад

    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

  • @ultragamer4465
    @ultragamer4465 Год назад

    GIGACHAD THANK YOU MY BROTHER

  • @AshleyHan-u4i
    @AshleyHan-u4i Год назад

    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

  • @tareq5264
    @tareq5264 2 года назад +1

    thank you man, you are a genius

  • @louissilsby8819
    @louissilsby8819 4 года назад

    I have been looking for so long for this exact kind of question, i messed this up in my exams. Thanks a bunch.

  • @admiremutero9036
    @admiremutero9036 4 года назад +2

    You a great teacher.
    Thank you sir

  • @chessandmathguy
    @chessandmathguy 3 года назад

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

  • @blalalalahd194
    @blalalalahd194 3 года назад

    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

  • @leanneteh8307
    @leanneteh8307 4 года назад +1

    tq for nailing things out, got so much clearer now

  • @Thabang_Kgatla1
    @Thabang_Kgatla1 4 года назад

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

  • @nifahadjiabobakar6402
    @nifahadjiabobakar6402 3 года назад

    How about for all positive integers n?

  • @betul1445
    @betul1445 Год назад

    What is mean 7m i did not got it

  • @kimberleysinclair7140
    @kimberleysinclair7140 2 года назад +1

    Thank you, great explanation

  • @mo7.998
    @mo7.998 3 года назад

    if i got 7(9m+2^k+2) as a proof is it ok ? or it just has one solution ?

  • @tariromakombe7914
    @tariromakombe7914 2 года назад +1

    Brilliant

  • @SkylanderBlazier
    @SkylanderBlazier 4 года назад +2

    Wow this was so helpful!

  • @freakx198
    @freakx198 Год назад +1

    amazing

  • @realndu
    @realndu 2 года назад +1

    Legend!!

  • @sebalizarraga1051
    @sebalizarraga1051 3 года назад

    awesomeee

  • @neilbhavikatti6720
    @neilbhavikatti6720 4 года назад +4

    Thanks so much!!!

  • @alexreynolds9710
    @alexreynolds9710 2 года назад +1

    thank you the math sorcerer!

  • @고민석-d3w
    @고민석-d3w 4 года назад +2

    Amazing!

  • @littlethphuong1840
    @littlethphuong1840 3 года назад +1

    thank you

  • @jacknyirenda7237
    @jacknyirenda7237 2 года назад

    This helped. Thank you.

  • @jemanvirk
    @jemanvirk 3 года назад +1

    Thanks sir

  • @ahmedlutfi4894
    @ahmedlutfi4894 Год назад

    beautiful

  • @farhanfarooq9074
    @farhanfarooq9074 3 года назад +1

    love from Pakistan

  • @sasukeutchiwa3600
    @sasukeutchiwa3600 3 года назад

    Tnx sir

  • @markcarranza2032
    @markcarranza2032 Месяц назад

    Wow

  • @ianmi4i727
    @ianmi4i727 4 года назад +1

    Calculus I !!! :)

  • @sakshu6549
    @sakshu6549 2 года назад

    👍

  • @aniketvasu1722
    @aniketvasu1722 3 года назад

    Thanks Man

  • @cpw1769
    @cpw1769 2 года назад

    Thx

  • @tymzon7446
    @tymzon7446 8 месяцев назад

    i love you

  • @franzsenkelo6246
    @franzsenkelo6246 10 месяцев назад

    Bad teaching

  • @uscybercom6009
    @uscybercom6009 Год назад

    Thx Bro👍

  • @siggimatti1129
    @siggimatti1129 2 года назад

    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!

    • @siggimatti1129
      @siggimatti1129 2 года назад

      to further explain he gets 9 and 2 but I get 81 and 25 so it's a bit more complicated