Power Series

What is a series? What are some tests used to determine whether an infinite series converges or
diverges? What is a power series? What are some tests used to determine whether a power series converges on
a particular domain? How can power series be applied to the study of differential equations? Given a series that
converges how can a finite value be assigned to it in general? What is the intuitive motivation for Ces`aro summation?
Are there series that are divergent when looking at the sequence of partial sums, but yet have a finite Ces`aro sum?
(Basically just answers these questions, and related with “real-analysis” in Math)

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The goal of this assignment is for you to pick out a topic of your choice and explore the said topic. By design
all material in mathematics usually has many theorems and results that can be discussed, but the goal is to pick out some
themes and enough details so as to be able to provide enough information for a formal write-up.
The write-up should contain:
– a title
– your name, the university’s name, and the due date
– an abstract
– an introduction
– sections (the breakup of which completely depends on the topic chosen)
– properly labeled lemmas, theorems, proofs, corollaries, examples, etc…
– a conclusion
– references
Grade Breakup: The total is 100 points.
5 Points: Title, Name, University Name, Due Date, and Confirmation of Minimum Length of 7 Pages
10 Points: Abstract
10 Points: Introduction
10 Points: Conclusion
5 Points: References

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