Timeline for For calculus students, what should be the intuition or motivation behind series?
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| Apr 2, 2014 at 23:00 | comment | added | Benjamin Dickman | Going beyond: If you are walking in steps of size $\frac{1}{n}$, then you will "walk off to infinity" (since you have the harmonic series). If you take steps of this size but rotate 180 degrees after each one, then you will converge to some point (since you have the alternating harmonic series). If you rotate 90 degrees after each step, then you will be walking in a sequence of nested squares, where the area of the squares becomes arbitrarily small; so you will converge to some spot (by a "nested square" property). More generally, see this MO post: mathoverflow.net/q/109582/22971 | |
| Apr 2, 2014 at 22:16 | history | edited | Brendan W. Sullivan | CC BY-SA 3.0 |
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| Apr 2, 2014 at 22:10 | history | answered | Brendan W. Sullivan | CC BY-SA 3.0 |