Andrzej Kukla

Master of Mathematics, with honours! 🥳

Cool non alternating series to calculate, what else would you like to do on this beautiful Sunday evening? Have fun! 👑

More floor = more fun 🧠 The original problem contained less floor and that was awful. I fixed it. And made it harder. Your welcome 😈

No but seriously, didn’t know this series would be so fun to evaluate. Have a nice Sunday!

First one is 2

game recognizes game

@hbou None of these, it’s a complex number, so you can’t compare it’s value to 0.

@Mathinity_ actualy how much is that? pi^(e*i)+1

After 250 years of silence, Euler finally shared a sequel to the famous Euler’s Identity 💀 Well… that’s obviously a joke, because Euler wasn’t silent for the past 250 years, but only 243. Oh, the identity? Yeah, this part it true actually, check it out for yourself!

If you solved previous Sunday Challenges, this one shouldn’t be any problem for you. Always great to see number theory on such contests 😊

Floor function and integral is a mix from hell that often leads to beautiful results. And this integral is a great example. Have fun! 🔥

Continue celebrating π-day with this fun little integral! 🥳❤️ have fun! π-day never ends.

@INSPECTOLNZ Ok, then my proof must be wrong. Can you point in which point it doesn’t hold?

@Mathinity_ Even a smaller value of actual «π»=π⁷⁶² is defined exactly: 0.999999(∞) is a fraction ¹/₁ This is why π is rational.

Happy π-day! 🥳 To celebrate this day I’ve decided to show you how to prove the irrationality of π! What is your favourite thing related to π? 🤔 Meanwhile, have a nice read! 🧵[1/8]

Simple! Apery’s proof that ζ(3) is irrational can be modified to show that ζ(2)=π²/6 is irrational, by constructing sequences of integers Aₙ and Bₙ 0 ≠ ζ(2)-Aₙ/Bₙ = ο(1/Bₙ) from which it follows that π² is irrational and hence π is irrational.

Thanks for reading! Have a great π-day! 🥳❤️ 🧵[8/8]

Second and last part of the proof. 🧵[7/8]