integral floor 1/sqrt x

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  • Опубликовано: 7 янв 2025

Комментарии • 14

  • @Mathematiker_KV
    @Mathematiker_KV День назад +6

    This can be recognised as the result of applying Abel's Summation formula (often used in analytic number theory). Make the substitution t = x^(-1/2) and we have 2 \int_1^\infty [t]/t^3 dt. This is equal to the sum from n = 1 to \infty of 1/n^2. The extra term [x]/x^2 vanishes as x tends to \infty. The sum equals pi^2/6 due to a result by Euler.

    • @drpeyam
      @drpeyam  День назад +1

      Thanks so much!!

  • @nameless1571
    @nameless1571 День назад

    Thank you for showing us this. I think it's very cool also!

  • @matrixstuff3512
    @matrixstuff3512 2 дня назад +2

    I love this!

  • @the.lemon.linguist
    @the.lemon.linguist День назад +4

    you forgot the dx in the thumbnail!

    • @k0pstl939
      @k0pstl939 День назад +1

      His arm was covering it /hj

  • @slavinojunepri7648
    @slavinojunepri7648 День назад

    Fantastic

  • @artichaug1719
    @artichaug1719 4 часа назад

    Why in the 90s nobody ever mentioned floor functions in math classes?

  • @anuragbundela1483
    @anuragbundela1483 2 дня назад +13

    Thank you my nigga dr peyam

  • @Arnav2322
    @Arnav2322 День назад +1

    Thanks

  • @pesilaratnayake162
    @pesilaratnayake162 День назад

    Pretty nice solution. I thought the problem was for round(1/sqrt(x)). Isn't that what [ ] means? I thought floor was |_ _|. Is that not the convention?

    • @drpeyam
      @drpeyam  День назад +1

      The convention is that [ ] and |_ _|mean floor

    • @pesilaratnayake162
      @pesilaratnayake162 9 часов назад

      @drpeyam good to know. I get confused with the symbols. Is ceil(x) |`x'| ? (Imagine ` is a horizontal line at the top, like a "bar")