#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

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

Look, if you just square this term, you can avoid an infinite series. It's Pythagoras, it's 2500 years old, just square it #pythagoras #infiniteseries

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

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

#math #calculus #infiniteseries #series

Something for your AP/Calc2 students...

1 - 1/3 + 1/5 - 1/7 +...
(a) Write this series in summation notation
(b) Explain why it converges.
(c) Using Wolfram Alpha or similar technology, calculate the sum of the 1st 1000 terms to 4 places.
(d) What is the approximate % error in using this partial sum to approximate π/4. Impressed or not?
(e) What is the connection between the inf series and π/4?
(f) Questions/Ideas?

#math #calculus #infiniteseries #series

Something for your AP/Calc2 students...

1 - 1/3 + 1/5 - 1/7 +...
(a) Write this series in summation notation
(b) Explain why it converges.
(c) Using Wolfram Alpha or similar technology, calculate the sum of the 1st 1000 terms to 4 places.
(d) What is the approximate % error in using this partial sum to approximate π/4. Impressed or not?
(e) What is the connection between the inf series and π/4?
(f) Questions/Ideas?