# Tag Info

### Examples of arithmetic and geometric sequences and series in daily life

I tutored a student who came with a kind of problem I had never seen before and found quite refreshing. It was something like: A child is being pushed on a swing by their father, reaching a maximum ...
Accepted

### What strategy for picking convergence tests for series do you teach?

I made this flowchart for my students last time I taught this stuff. Not the best visually, but I think it effectively conveys my thought process.
Accepted

### What strategy for picking convergence tests for series do you teach?

First, let's ignore geometric series and $p$-series because those are standard examples. For infinite series with positive terms, if you really understand how sequences grow then almost all examples ...

### Proof that convergent Taylor Series converge to actual value of function

If the power series $\sum_{j=0}^\infty a_j z^j$ converges to some function $f(z)$, then the Maclaurin series of $f(z)$ is $\sum_{j=0}^\infty a_j z^j$. But the converse need not hold. It could happen ...

### Comparison Tests in Calculus

I tend to teach option (2.) for many of the reasons already listed in the existing answers. If we just teach (1.) then the problem solving becomes formulaic which means the whole endeavor is ...

### Examples of arithmetic and geometric sequences and series in daily life

When I think of a geometric sequence, I think of something where the initial input value = 1, not 0. Most interest problems would start at time = 0, so I would exclude these unless you said something ...

### 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 ...

### For calculus students, what should be the intuition or motivation behind series?

The fact of the matter is series is sort of viscerally off the beaten track of limits/derivatives/minmax apps/integral toolbag/integral apps. It's there because it is needed later (and covered more) ...

### Comparison Tests in Calculus

I think we should at least mention direct comparison, and show a brief example like $\sum \frac{1}{x^2+1} < \sum \frac{1}{x^2}$, because that seems like the most straightforward way for students to ...