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11 votes
Accepted

Motivating example for sequences, sums and limits in high school

This application is known as "gross-up" in accounting. You run the finances for a small business. The boss would like to give an employee a \$100 bonus for their hard work. However, the ...
Chris Cunningham's user avatar
9 votes

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

The concept of a limit has nothing to do with the order on $\mathbb{R}$. The standard definition of a limit of a sequence generalizes, almost verbatim, to sequences with values in $\mathbb{R}^n$, ...
Kostya_I's user avatar
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7 votes

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

I don't like it. Had a hard time following it. Just tuned out. Yes, I'm not a Ph.D. in math. But neither will be the target students. You should have won me over. You didn't. I have the IQ to ...
guest's user avatar
  • 199
6 votes

Motivating example for sequences, sums and limits in high school

I'm not sure that starting with an applied motivation (derivation, word problem) is the best way to introduce this topic. Look at how your experiment failed. This is because "word problems are ...
guest troll's user avatar
5 votes
Accepted

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

The linear function component is covered early(ish) in Algebra 1, and quadratic functions are covered towards the end of Algebra 1; so, the former by 7th/8th grade and the latter - if at all - by 8th ...
Benjamin Dickman's user avatar
5 votes

Teaching limits of sequences before limits of functions in Calculus?

To explain the answer, I found this question while thinking about asking a similar question. In teaching both pre-calculus and calculus, this is an issue that seems to come up over and over again in ...
Xander Henderson's user avatar
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3 votes

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

I think the answer depends on the meta question: why are students learning the definition of a limit? Here are some reasons I can think of: Because students are taking an intro-to-proofs class and ...
Jason Siefken's user avatar
3 votes

Motivating example for sequences, sums and limits in high school

There are lots of good physics examples involving equilibrium. For example, you can set up a pendulum and show how the amplitude forms a sequence that decays exponentially toward zero, or describe ...
user17655's user avatar
3 votes

Motivating example for sequences, sums and limits in high school

The common puzzle of giving a few terms and asking for the next are examples of (generating) sequences by some particular rule. A series is just a sequence, summed together. Ask e.g. for the sum $1 + ...
vonbrand's user avatar
  • 12.3k
3 votes

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

Here is a simpler definition of limits which works better for monotone sequences, and has value in motivating further investigation of the concept of limits: If a sequence $x_1, x_2, ...$ is ...
kaya3's user avatar
  • 529
3 votes

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

While monotone behavior is important in analysis (such as the monotone convergence theorem in measure theory), I think you should forget the emphasis on monotone behavior and just be honest with the ...
KCd's user avatar
  • 3,536
3 votes

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

This is a topic I could imagine not being adequately covered in all U.S. schools, although (as Dave L. Renfro pointed out in a comment), it is listed in the Common Core Mathematics standards under ...
Daniel R. Collins's user avatar
3 votes

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

ADVICE: When you have a question about a speech, you should give us more information to help you. Especially how long is the speech (it affects how much intro you do). But also the audience. And ...
guest's user avatar
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2 votes

Motivation for Fibonacci: Bees

After looking at Tony Jacobs argument, here is an argument of my own. Start with a single male. At each generation, let $m_n$ and $f_n$ be the total number of males and females respectively, and let ...
Martin Argerami's user avatar
2 votes
Accepted

Motivation for Fibonacci: Bees

You can see it by breaking the numbers $s_n$ into parts: $s_n=f_n+m_n$, which represent the number of female and male bees, respectively, at each level of the family tree. To find $f_{n+1}$, we note ...
G Tony Jacobs's user avatar
2 votes

What is the intuition behind the limit superior?

For me, this picture from wikipedia helped the most in understanding limsup and liminf
Adam Rubinson's user avatar
1 vote

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

Two points to think about: It might be more intuitive to replace "from some $N$ onward" by "for all $n$ except finitely many". I often present the notion of a limit through a game:...
Raz Kupferman's user avatar
1 vote

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

First answer: Isn't sequence like a list of numbers that appear as according to function? And series is more like the addition of the terms of the sequence. I guess There convergence properties differ ...
Karan Bhasin's user avatar
1 vote

What is the intuition behind the limit superior?

Limit supremum (of a sequence of numbers) I will try to give intuition only using words, without using mathematical symbols. What is the smallest number which is greater than infinitely many members ...
Nilotpal's user avatar
1 vote

Any metaphors/intuitions for a limit of a sequence?

Here is my "unfinished" attempt that I used in one of my classes last year. Generally speaking, it is based on the idea of "proof-generated definitions" introduced by Lakatos. As such, the question is ...
Amir Asghari's user avatar
  • 4,438

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