#infiniteseries — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #infiniteseries, aggregated by home.social.
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Achilleus: "Can't outrace a tortoise," huh? Well, tough guy, why don't you come over HERE and say that?
Zeno of Elea: ... 🤗 🤓
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Achilleus: "Can't outrace a tortoise," huh? Well, tough guy, why don't you come over HERE and say that?
Zeno of Elea: ... 🤗 🤓
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Achilleus: "Can't outrace a tortoise," huh? Well, tough guy, why don't you come over HERE and say that?
Zeno of Elea: ... 🤗 🤓
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Achilleus: "Can't outrace a tortoise," huh? Well, tough guy, why don't you come over HERE and say that?
Zeno of Elea: ... 🤗 🤓
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Achilleus: "Can't outrace a tortoise," huh? Well, tough guy, why don't you come over HERE and say that?
Zeno of Elea: ... 🤗 🤓
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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
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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
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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
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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
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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
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“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.”
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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
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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
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#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? -
#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? -
#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?