Science:Infinite Series Module/Syllabus/The IST

The Infinite Series Test (IST) consists of 20 questions, is marked out of 30, and students will have 120 minutes to complete the test. The test

• will be proctored by the TA in a lab on campus
• will be administered through WeBWorK
• is a closed book test (no calculators or additional aids will be permitted)

Some questions are worth more than others. The number of questions that appear on the IST for each topic is given in the table below.

The IST will be offered at most once per semester. Students can take the IST as many times as they like, but only once per semester.

Learning Objectives

On the IST, students will be expected to demonstrate their ability to meet the following learning objectives through WeBWorK.

• Given an infinite sequence
  • determine if the sequence converges
  • calculate limiting values of convergent sequences
• Given an infinite series
  • choose which convergence test is appropriate to establish if the series converges
  • determine whether or not the series converges
  • if the series converges, determine what it converges to
• Apply concepts of convergence testing to power series to determine their radius and intervals of convergence

Practice Test

Students who are preparing for the IST can download a practice test and its solutions here (test not available yet).

This test will give students a sense of what types of questions will be asked on the IST, as well as an idea of the difficulty of the test. This test will also become available in WeBWorK. For those students who are not familiar with WeBWorK, it is recommended that students use this test to familiarize themselves with the WeBWorK environment prior to taking the IST.

Topics Covered on the IST

The topics that will be on the IST can be organized into four different 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
  • p-series
• Unit 2: Convergence Tests
  • divergence test
  • integral test
  • alternating series test
  • absolute convergence
  • ratio test
• Unit 3: Power Series
  • definition of the power series
  • interval of convergence
  • Taylor and MacLaurin series
  • differentiation and integration of power series
• Unit 4: Review

Topics Not Covered on the IST

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

Writing the IST

Information regarding where and when the test will take place will be posted on the announcements page.

What to Bring

Students can bring pencils or pens to write with.

Paper will be supplied for rough work, but rough work will not be graded.

Students must bring their UBC student card in order to write the IST.

Formula Sheet

Before the test begins, each student will receive a handout with the following formulas:

${\begin{aligned}e^{x}&=\sum _{k=0}^{\infty }{\frac {x^{k}}{k!}}\\\sin(x)&=\sum _{k=0}^{\infty }(-1)^{k}{\frac {x^{2k+1}}{(2k+1)!}}\\\cos(x)&=\sum _{k=0}^{\infty }(-1)^{k}{\frac {x^{2k}}{(2k)!}}\\\tan ^{-1}(x)&=\sum _{k=0}^{\infty }(-1)^{k}{\frac {x^{2k+1}}{(2k+1)!}}\end{aligned}}$

Other Details

Students will not necessarily be asked to determine whether a given series converges using a particular convergence test.

It may be up to the student to determine which test is appropriate.

Students writing the IST should be able to find partial fraction decompositions of rational functions.

Students will not be expected to use l\'Hospital\'s Rule on the IST.