# Questions tagged [series]

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### Generating function example

I'm about to introduce the Generating Function concept to a couple of kids. The plan is just to roughly follow Herbert Wilf's Generatingfunctionology's first 12 pages, until Fibonacci numbers and Ch 1....
2k views

### How can we explain intuitively the convergence and divergence of these two series?

It is known that $\displaystyle\sum_1^{\infty} \frac{1}{n^{1.000001}}$ converges while $\displaystyle\sum_{n\text{ is a prime number}}\frac{1}{n}$ diverges. Though we can logically prove these results,...
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 ...
212k 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 ...
181 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 ...
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 ...
1 vote
277 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. ...
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 ...