# 2019 CED Unit 10: Infinite Sequences and Series

Unit 10 covers sequences and series. These are BC only topics (CED – 2019 p. 177 – 197). These topics account for about 17 – 18% of questions on the BC exam. Topics 10.1 – 10.2 Topic 10.1: Defining Convergent and Divergent Series. Topic 10. 2: Working with Geometric Series. Including the formula for the sum…

# Power Series 2

This is a BC topic Good Question 16 (11-30-2018) What you get when you substitute. Geometric Series – Far Out (2-14-2017) A very interesting and instructive mistake Synthetic Summer Fun (7-10-2017) Finding the Taylor series coefficients without differentiating Error Bounds (2-22-2013) The alternating series error bound, and the Lagrange error bound The Lagrange Highway (5-20-15)…

# What Convergence Test Should I Use? Part 2

In last’s Friday’s post I really didn’t answer this question. Rather, I tried to show that there is not only one convergence test that must be used on a given series. Nevertheless, the form of a series suggest a test that is likely to work. In this post, I’ll try to give some suggestions as…

# Which Convergence Test Should I Use? Part 1

One common question from students first learning about series is how to know which convergence test to use with a given series. The first answer is: practice, practice, practice. The second answer is that there is often more than one convergence test that can be used with a given series. I will illustrate this point…

# Error Bounds

How Good is Your Approximation? Whenever you approximate something you should be concerned about how good your approximation is. The error, E, of any approximation is defined to be the absolute value of the difference between the actual value and the approximation. If Tn(x) is the Taylor/Maclaurin approximation of degree n for a function f(x)…