Worksheets/Infinite Series Convergence: Difference between revisions
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\sum_{i=1}^{\infty} \dfrac{1}{n^2} = \dfrac{\pi^2}{6} | \sum_{i=1}^{\infty} \dfrac{1}{n^2} = \dfrac{\pi^2}{6} | ||
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Explore a couple of methods of calculating pi, compare the results of a few methods, compare the computational cost. Push the limits. | |||
=References= | =References= | ||
Revision as of 00:51, 11 May 2016
In this worksheet we study the convergence behavior of the series:
$ \sum_{i=1}^{\infty} \dfrac{1}{n^2} = \dfrac{\pi^2}{6} $
Explore a couple of methods of calculating pi, compare the results of a few methods, compare the computational cost. Push the limits.
References
Basel problem: https://en.wikipedia.org/wiki/Basel_problem
Proving the series converges (multiple ways): https://www.youtube.com/watch?v=9euTxoCC8Hk
Background on other convergent series: https://plus.maths.org/content/infinite-series-surprises
Ways of calculating pi: http://pi3.sites.sheffield.ac.uk/tutorials/week-7
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Link to all worksheets idea list: Worksheets
Calc II:
- Archimedes: Don't Disturb my Circles Worksheets/Archimdes_Dont_Disturb_My_Circles
- Simpson's Rule: Worksheets/Simpsons_Rule
- Civil Engineering Road Planning: Worksheets/Civil_Engineering_Road_Planning
- Euler's Method and Circuits: Worksheets/Eulers_Method_Circuits
Calc III:
- Infinite Series: Worksheets/Infinite_Series_Convergence
- Partial derivatives: Worksheets/Van Der Waal Equation Critical Point