Questions tagged [series]
The series tag has no usage guidance.
12
questions
-2
votes
1
answer
154
views
Finite sum of infinite series
I have two issues related to finite sum of infinite series,
1) How you would to describe 2 when you talk about the infinite geometric series 1+ 1/2 + 1/4 + 1/8 + .....
2) How you would compare using ...
- 755
7
votes
6
answers
1k
views
Motivating example for sequences, sums and limits in high school
I currently work as a substitute teacher at a local high school and the topic in one of the classes is sequences, series and limits. Because I always disliked learning about a topic without having ...
- 73
1
vote
1
answer
212
views
Intuition explanation about Lebesgue measure zero of the rational numbers [closed]
This is a question about the intuition of the rational number having measure zero. Let us consider followng proof:
Let $I = [0,1]$ and $Q = \mathbb Q \cap I$ and let $\lambda$ be the Lebesgue measure. ...
- 379
4
votes
5
answers
1k
views
What strategy for picking convergence tests for series do you teach?
Without getting bogged down in details, I'll list the names only. It seems that the strategy I generally use is this:
Divergence test first
Is it a recognizable form? p-series or geometric?
a) No ...
user13544
2
votes
4
answers
864
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
$$\operatorname{erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{t^2} dt = \frac{2}{\sqrt{\pi}}\sum_{n=0}^{\infty}...
- 121
5
votes
8
answers
581
views
Comparison Tests in Calculus
How should I teach Comparison Tests in Calculus II, and why?
Note that I will cover comparison tests in some way, and students will be expected to justify their answers to questions about series ...
- 20.8k
9
votes
7
answers
208k
views
Examples of arithmetic and geometric sequences and series in daily life
In this part of the course I am just trying to show that we actually see a lot of sequences and series every day in our regular life.
I already found some examples such as the house numbers when you ...
- 383
8
votes
5
answers
963
views
Geometric Series Formula and Calculus
Is there any good reason that in educational materials, I consistently see the formula for calculating geometric series in canonical form as:
$$\sum_{k=0}^{n-1} ar^k = a \frac{1-r^n}{1-r}$$
While an ...
- 2,586
11
votes
6
answers
1k
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 ...
- 1,235
13
votes
8
answers
5k
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 ...
- 1,748
32
votes
12
answers
5k
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 ...
- 11.3k
32
votes
11
answers
8k
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 ...
- 11.3k