Math's conjectures

~ We're excited to present you this time with some new inequalities attacked by Muirhead - AM|GM - Bergstrom ('s) ineqs and homogeneity method ~

Warning: May cause extreme brain growth. New set of inequalities inside! Including: AM-GM inequality, Radon's inequality, tangent line trick and more coming soon. "The limit does not exist... for these inequalities." 🔥

https://www.cut-the-knot.org/m/Algebra/RadonInequality.shtml

For those who're calculus lovers, this is specifically for you 😉

Just enjoy!

My new collection of some elegant (not-too-hard) inequalities from RMM group. Hopefully you all will like it! 😊

A new, synthesis challenge requiring a comprehensive understanding of calculus. The solution climaxed with a rather tricky substitution due to the rotational symmetry of the limit point, specially 0 in this case:

🌺 Hey there, my wonderful tribe! 💕 Today, as we celebrate the incredible magic of womanhood, I want to take a moment to get real and raw with you. 🙏

There was a time in my life when I felt like I was drowning in a sea of uncertainty and pain. 💔 But you know who threw me a lifeline? A group of badass women who refused to let me sink! 🚣‍♀️ These fierce souls held my hand, dried my tears, and reminded me of the unbreakable strength that lies within every woman. 💪

Today, I want to give a massive shoutout to all the women out there who have been through hell and back, yet still manage to radiate love and light wherever they go. 🌞 You, my darlings, are the true warriors of this world!

As I think about the wild and beautiful journey of being a woman, I can't help but feel a rush of pride and amazement. 🌈 We've smashed through glass ceilings, shattered stereotypes, and dared to dream bigger than ever before. 🌠 From the trailblazers who paved the way to the everyday sheroes who inspire us with their courage and compassion, each one of you is a force to be reckoned with! 🔥

So, on this International Women's Day, I want you to know that you are a freakin' masterpiece, a work of art crafted by the hands of the universe itself. 🎨 Embrace your quirks, celebrate your wins, and never forget the incredible power you hold within. 💖

To all the women who have left an indelible mark on my soul and to those I haven't had the pleasure of meeting yet - thank you for being the wild, wonderful, and awe-inspiring beings that you are. 😊 Let's keep lifting each other up, cheering each other on, and creating a world where every woman can thrive! 🌍

Here's to the women who move mountains, shatter expectations, and make the world a better place just by being themselves! Happy International Women's Day, my fierce and fabulous tribe! 🌷

My new series of some common calculus problems/exercises. May your day traverse smoothly towards positivity, converging optimally at joy!

New year highlight: "A surprisingly neatly closed form for a MSE problem (https://math.stackexchange.com/questions/4834174/prove-the-zeta-log-gamma-integral-int-01-zeta1-n-1-t-ln-gammatdt-f/4837618?fbclid=IwAR0NW04j2PgUaxOQD-m3O0C3ckr0IS6T9Q-sRf2C71sQWSTeNrnQupjohQY #4837618) - employing some initially tricky steps"

Another idea is given by sir Fao Ler (https://www.facebook.com/100038384963463/posts/1075724597050362/?app=fbl)

As the clock strikes midnight and confetti rains down, I take a moment to reflect on the incredible journey we shared in 2023. Your love, support, and uplifting math problems have been my greatest treasures. In the year to come, I promise to keep pouring my heart into this space, sharing things that inspire, connect, and maybe even make you shed a happy tear or two. So grab a comfy seat, my dearest fellows, because 2024 is about to unfold, and I can't wait to see what adventures we embark on together. ✨

Tackling a merely symmetric limit exercise by the so-called "King Rule" trick applied for series, along with a highly effectively eclectic definition of the exponential function e^x :

Embarking upon the dawn of a new day, I am eager to unravel the enigmatic allure of two delightful riddles that shall ignite my intellectual curiosity and set ablaze the fires of my mind...