Homework 5

Due: Feb 24th, 2021

Our next topic in class will be sequences and series of functions. These exercises are on sequences and series of numbers.

Exercises

  1. Lebl 2.2.12

  2. Choose one: Lebl 2.2.14, 2.2.15

  3. Lebl 2.5.14. What if we drop the assumption \(x_n \geq 0\)?

  4. Choose one: TBB 1.11.6, 2.14.1-3, 2.14.8, 2.14.10, 3.12.1, 3.12.8-11. (Some of these are quite challenging. I hope you will enjoy trying as many of them as possible. Probably 2.14.1-2, 2.14.8 are less challenging than the others.)

Instructions

If you don’t have LaTeX on your computer, you can use Overleaf. Upload the PDF to Gradescope. Don’t submit the LaTeX source, just the PDF.

  • When you upload to Gradescope, please mark which page of the PDF has your answer to each question!

Email your instructor (that’s me) if you have questions or need help.

Some additional formatting instructions are in the syllabus. To summarize:

  • Use a new page (\newpage) for each problem.
  • State which question you are answering and the actual question. Then, start your answer in a new paragraph.
  • Use environments such as proof and theorem (via \begin{proof}...\end{proof}).
  • Use 12pt option \documentclass[12pt]{amsart} and \linespread{2.4}.

Please find and use the LaTeX template linked on the course website.

You are encouraged to work together on the homework!

Additional reading