Legendary 2024 MIT Integration Bee Final Round Integral Problem

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  • Опубликовано: 23 дек 2024

Комментарии •

  • @mathnerd5647
    @mathnerd5647 15 дней назад +3

    Absolutely the best integral video and explanation I've watched this year

    • @drpkmath12345
      @drpkmath12345  14 дней назад

      Haha thanks a lot my friend for your support👍👍👍

  • @ronbannon
    @ronbannon 15 дней назад +5

    Yikes, I worked on this problem, too! I thought it was not a problem at first, but it just kept getting more problematic as I proceeded. I could not fathom doing this under a time constraint.

    • @domedebali632
      @domedebali632 15 дней назад +1

      Yikes, I tried this with an estimated (and anticipated time) of like 30 minutes but took me more than 2 hours uh

    • @ronbannon
      @ronbannon 15 дней назад

      @@domedebali632 I followed a lot of deadends myself. Finally figured it out.

    • @drpkmath12345
      @drpkmath12345  14 дней назад

      Ohhh haha yes this took longer than I thought, too👍👍👍

  • @filipeoliveira7001
    @filipeoliveira7001 16 дней назад +4

    For an intuitive method of tackling the last step (the infinite product), and most likely the method they used in the competition, you can separate it into product[(n+1)/(n-1)] * product[(n^2-n+1)/(n^2+n+1)] and make it the product from 2 to K where K -> infinity. Then, you can see that the first part of product will be ((K+1)!/2)/(K-1)! = (K^2+K)/2. For the second part of product, Define the sequence a_n = n^2 - n + 1 and you’ll see that a_(n+1) = n^2 + n + 1 so the second part equals product[ a_n / a_(n+1) ] and telescoping the product yields (a_2)/(a_(K+1)) = (4-2+1)/(K^2 + K + 1) = 3/(K^2+K+1). Putting the two together yields Product = lim K -> +inf [ 3(K^2 + K)/2(K^2 + K + 1) = 3/2

    • @ronbannon
      @ronbannon 15 дней назад +2

      I'm not sure why RUclips doesn't support LaTeX-like input, as hints like yours would be way easier to read if it did. In any case, thanks for sharing.

    • @domedebali632
      @domedebali632 15 дней назад

      @@ronbannon that's right. RUclips should support LaTeX or similar inputs

    • @filipeoliveira7001
      @filipeoliveira7001 15 дней назад

      @@ronbannon yeah, sorry if it’s a bit messy. I hope it was still comprehensible!

    • @filipeoliveira7001
      @filipeoliveira7001 15 дней назад

      @@ronbannon I’m still in high school so I don’t have a good deal of experience using mathematical notation over the internet / in forums such as stack exchange

    • @ronbannon
      @ronbannon 15 дней назад +1

      @filipeoliveira7001 Wow, you're a great student. I was not complaining about your comment, I was noting that RUclips needs to support LaTeX!

  • @Min-cv7nt
    @Min-cv7nt 16 дней назад +4

    Awesome video professor

    • @drpkmath12345
      @drpkmath12345  14 дней назад

      Thank you so much my friend haha👍👍👍

  • @MrGLA-zs8xt
    @MrGLA-zs8xt 16 дней назад +3

    You are the best professor

    • @drpkmath12345
      @drpkmath12345  14 дней назад

      Thanks a lot my friend haha 👍👍👍

  • @domedebali632
    @domedebali632 16 дней назад +4

    You are like integration God

    • @drpkmath12345
      @drpkmath12345  14 дней назад

      Haha thanks a lot my friend👍👍👍

  • @tarentinobg
    @tarentinobg 16 дней назад +1

    awesome. I love using sigma notations when doing integrals. Thanks Doc PK

  • @iqtrainer
    @iqtrainer 16 дней назад +4

    Sooo cooolll🎉

  • @LITHICKROSHANMS-gw2lx
    @LITHICKROSHANMS-gw2lx 15 дней назад +2

    Ok good solution sir
    When will you upload integral advanced techniques and method to solve

    • @drpkmath12345
      @drpkmath12345  14 дней назад

      Thank you my friend for your comments?m! Pulling those up now👍👍👍