Science:Infinite Series Module/Syllabus

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The infinite Series Module (ISM) is a set of assessments and teaching resources that support students in acquiring knowledge and skills in working with infinite sequences and series.

The ISM has no formal instructor. UBC students who have questions regarding infinite series are encouraged to contact their instructor or TA.

Topics Covered in the ISM

The topics in the ISM is be organized into the following "units".

  • Unit 1: Introduction to Infinite Sequences and Series
    • definition of an infinite sequence
    • definition of convergence of an infinite sequence
    • sigma notation
    • shifting the index of summation
    • definition of convergence of an infinite series
    • geometric series
    • harmonic series
    • telescoping series
  • Unit 2: Convergence Tests
    • divergence test
    • integral test and the p-series
    • alternating series test
    • ratio test
  • Unit 3: Power Series
    • definition of the power series
    • interval of convergence
    • Taylor and MacLaurin series

Topics Not Covered in the ISM

Students will not be expected to be familiar with

  • remainder estimation techniques
  • the limit comparison test for convergence of infinite series
  • the comparison test for convergence of infinite series
  • the root test for convergence of infinite series
  • the formal definition of limit for sequences and series
  • the binomial theorem