Questions tagged [sequences]
The sequences tag has no usage guidance.
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What kind of sequence is between an arithmetic and a geometric sequence?
In school we teach arithmetic and geometric sequences. Students should notice that arithmetic sequences (with common difference greater than $0$) grow steadily, while geometric sequences (with common ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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: http://www.stitz-zeager.com/szprecalculus07042013.pdf
However, it does not cover ...
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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 \...
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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 ...
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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 ...
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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 ...
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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 ...
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