Dm07 Sequencesseries Seriesexample Ipynb Github

There was an error while loading. Please reload this page. There was an error while loading. Please reload this page. Welcome to the public repo for this course. Below is the list of assignments and ungraded labs course-wise.

At the time we are not accepting Pull Requests but if you have any suggestion or spot any typo please raise an issue. If you find a bug that is blocking in any way consider joining our community where our mentors and team will help you. You can also find more information on our community in this Reading Item within Coursera. In this lab, we will use SageMath to determine the convergence or divergence of a sequence of numbers and of infinite series. Consider the sequence {cos⁡(nπ)arctan⁡(n)}n=1∞\{\cos(n\pi)\arctan(n)\}_{n=1}^\infty{cos(nπ)arctan(n)}n=1∞​. We start by determining the first 10 terms of this sequence.

We can do this in SageMath by letting an=cos⁡(nπ)arctan⁡(n)a_n = \cos(n\pi)\arctan(n)an​=cos(nπ)arctan(n) and then using a for\textbf{for}for loop and the range\textbf{range}range command. We can get a better idea of what these numbers are by using the round\textbf{round}round command. Note that the terms of the sequence do not appear to approach a specific number. We can better tell what is happening by plotting the first 100 or so terms of the sequence. We can plot a point in SageMath by using the point\textbf{point}point command along with the show\textbf{show}show command. To plot multiple points on the same plot, we will store the points in a list and then show the list.

SageMath does not allow us to plug the list directly into the show\textbf{show}show command. Instead, we must input the sum of the elements in the list. From the graph, we see that the odd terms are approaching a specific value, namely −π2-\frac{\pi}{2}−2π​, and the even terms are approaching a specfic value, namely π2.\frac{\pi}{2}.2π​. However, since these values are different, the sequence diverges. There was an error while loading. Please reload this page.

There was an error while loading. Please reload this page. Below is the list of topics that are covered in this section: In this module, we define a sequence as an arrangement of an infinite number of numbers written in a specific order. The common notations used for a sequence are \(\left\lbrace a_n\right\rbrace = \left\lbrace a_n\right\rbrace_{n=1}^{\infty} = \left\lbrace a_1, a_2, \ldots \right\rbrace\), where \(a_i\) denote the \(i^{\text{th}}\) term of the sequence. Write the first 5 terms of the following sequences:

\(\left\lbrace \dfrac{1}{n} \right\rbrace = \dfrac{1}{1}, \dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}, \dfrac{1}{5}, \ldots\)

People Also Search

• DM07-SequencesSeries/SeriesExample.ipynb at master - GitHub
• GitHub - DiscreteMaths/DM07-SequencesSeries: Data Science 2018
• Lab 07 - Sequences and Series.ipynb - GitHub
• VictorCodebase/Sequences-Time-Series-and-Prediction - GitHub
• CoCalc -- Lab 07 - Sequences and Series.ipynb
• GitHub
• raw.githubusercontent.com
• Python-for-Data-Science-and-Machine-Learning-Bootcamp/02 ... - GitHub
• 8.7. Sequences and Series - GitHub Pages
• Lab 07 - Sequences and Series - Jupyter Notebook - CliffsNotes