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

Intuitively, to me, it means that if you take the positive number line, put a blue dot at every prime, and a red dot on all the the numbers of the form $n^{1.000000000001}$, then eventually, very far ...
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