Questions tagged [series]

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31
votes
11answers
7k views

How can I teach my students the difference between a sequence and a series?

Sequences and series are related concepts but differ extremely from one another. I feel that students in integral calculus frequently mix them up. Part of the problem is that: Sequences are usually ...
29
votes
11answers
4k views

For calculus students, what should be the intuition or motivation behind series?

I've noticed that series are one of the most difficult portions of calculus for new students to learn. I think the level of abstraction has to do with this. Limits, derivatives, and integrals, as ...
13
votes
8answers
3k views

What are some fun/nonstandard examples of arithmetic/geometric series?

I am teaching those topics (arithmetic/geometric series) just now, and want some not so standard (fun) examples, which can be used essentially at high school/beginning calculus level. I'm ...
11
votes
6answers
998 views

How can I convince students that Fourier series are useful?

Main question: Calculating the coefficients of a Fourier series can be difficult and time-consuming. How might a student be motivated/convinced to go through these (potentially tedious) details? Are ...
8
votes
5answers
772 views

Geometric Series Formula and Calculus

Is there any good reason that in educational materials, I consistently see the formula for calculating geometric series in canonical form as: $$\sum_{k=0}^{n-1} ar^k = a \frac{1-r^n}{1-r}$$ While an ...
7
votes
7answers
114k views

Examples of arithmetic and geometric sequences and series in daily life

In this part of the course I am just trying to show that we actually see alot of sequences and series everyday in our daily life. I already found some examples such as the housenumbers when you drive ...
5
votes
8answers
368 views

Comparison Tests in Calculus

How should I teach Comparison Tests in Calculus II, and why? Note that I will cover comparison tests in some way, and students will be expected to justify their answers to questions about series ...
2
votes
4answers
176 views

Proof that convergent Taylor Series converge to actual value of function

Taylor series (or Maclaurin Series) are the only way to get values for some functions, such as $$\operatorname{erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{t^2} dt = \frac{2}{\sqrt{\pi}}\sum_{n=0}^{\infty}...