Questions tagged [sequences]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3 votes
6 answers

Is this motivation for the concept of a limit a good one?

tldr: There is a simple intuitive definition of a limit for monotone sequences, and I suggest that it can be used to motivate the (more complicated) standard definition. I am asking for feedback on my ...
8 votes
6 answers

What is the intuition behind the limit superior?

I want to write an article which explains the limit superior. I also want to present the intuition behind this concept. Currently I would describe the limit superior as the "least upper bound of a ...
7 votes
6 answers

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 ...
33 votes
11 answers

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 ...
5 votes
2 answers

In what grade do kids (New York, US) learn common differences?

I'm teaching an after school workshop for a few 7th graders. I was having them try to predict the next item in a complicated sequence. After some failed attempts, one of the kids started analyzing the ...
19 votes
4 answers

Teaching limits of sequences before limits of functions in Calculus?

Most Calculus courses/textbooks I have seen teach the different topics in that order: limits of functions, continuity, differentiability, integration. Then, depending on the teacher/textbook's ...
1 vote
1 answer

How can I introduce a speech about the Fibonacci sequence creativiely?

I am a high school senior student. Soon, I am giving a presentation about the Fibonacci sequence and I am searching for a creative way to start my speech. I was wondering whether someone in this ...
5 votes
2 answers

Motivation for Fibonacci: Bees

I want to talk about the Fibonacci sequence in my Linear Algebra class. So I tried to look online for examples where the sequence appears naturally. One of the most often mentioned is that of the ...
22 votes
11 answers

What interesting properties of the Fibonacci sequence can I share when introducing sequences?

The Fibonacci numbers are one of the first sequences given as examples of sequences in many calculus textbooks as they have a definition that does not obviously have a closed form and they have many ...
8 votes
6 answers

Any metaphors/intuitions for a limit of a sequence?

I'm writing (together with a colleague) a minicourse on mathematical analysis (currently we want to cover the Weierstrass theorem on functions on compact intervals, so the aim is to present only the ...
10 votes
2 answers

Substitution in recurrence relations

Let's say we study a reccurence relation such as $$a_{n+1}=a_{n}+n, n \geq 1$$ I find many students are having difficulties when you ask them to find $$a_{n}$$ in terms of $$a_{n-1}$$ where they just ...
6 votes
4 answers

Are convergent and divergent sequences a prerequesite for calculus or are they a part of it?

Basically the textbooks in my country are awful, so I searched on the web for a precalculus book and found this one: However, it does not cover ...
18 votes
4 answers

What are your favorite instructional counterexamples on sequences?

In this article, I give counterexamples regarding real sequences. And in that one some others. In particular counterexamples answering questions like: "If for all $p \in \mathbb{N}$ $\lim\limits_{n \...