#infiniteseries — Public Fediverse posts

Achilleus: "Can't outrace a tortoise," huh? Well, tough guy, why don't you come over HERE and say that?

Zeno of Elea: ... 🤗 🤓

#zeno #achilles #infiniteSeries #badJokes

Let \(\varpi=\dfrac{\Gamma^2\left(\frac14\right)}{2\sqrt{2\pi}}=2.62205755\ldots\) be the lemniscate constant. Then,
\[\Large\displaystyle\sum_{n=1}^\infty\dfrac{1}{\sinh^4(\pi n)}=\dfrac{\varpi^4}{30\pi^4}+\dfrac{1}{3\pi}-\dfrac{11}{90}\]

#Series #Sum #InfiniteSum #LemniscateConstant #GammaFunction #Lemniscate #LemniscateOfBernoulli #Bernoulli #Math #Maths #InfiniteSeries #HyperbolicSines

“But synthetical reasoning, setting up as its goal some unattainable abstraction, like an imaginary quantity in algebra, and commencing its course with taking for granted some two assertions which cannot be proved, from the union of these two assumed truths produces a third assumption, and so on in infinite series, to the unspeakable benefit of the human intellect.”

https://library.hrmtc.com/2024/08/13/but-synthetical-reasoning-setting-up-as-its-goal-some-unattainable-abstraction-like-an-imaginary-quantity-in-algebra-and-commencing-its-course-with-taking-for-granted-some-two-assertions-which-ca/

An infinite sum consisting of Fibonacci numbers:

\[\displaystyle\sum_{n\geq0}\binom{2n}{n}\dfrac{F_n}{8^n}=\sqrt{\dfrac{2}{5}}\]

#FibonacciNumber #Fibonacci #FibonacciSequence #FibonacciNumbers #FibonacciSeries #InfiniteSum #InfiniteSeries #Sum #Maths #Math