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www.experimental-psychology.de | ||
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satoshi.nakamotoinstitute.org
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| | | | | Advancing and preserving bitcoin knowledge | |
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karltoepfer.com
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| | | | | On the Use of Google Translate in Writing a History of PantomimeDownload "On the Use of Google Translate in Writing a History of Pantomime," a small paper presented at the West Coast Germanists Workshop University of California Davis, March 17, 2018. | |
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www.icqpodcast.com
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www.jeremykun.com
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| | | Problem: $ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots = 1$ Solution: Problem: $ \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots = \frac{1}{2}$ Solution: Problem: $ \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \dots = \frac{1}{3}$ Solution: Problem: $ 1 + r + r^2 + \dots = \frac{1}{1-r}$ if $ r < 1$. Solution: This last one follows from similarity of the subsequent trapezoids: the right edge of the teal(ish) trapezoid has length $ r$, and so the right edge of the neighboring trapezoid, $ x$, is found by $ \frac{r}{1} = \frac{x}{r}$, and we see that it has length $ r^2$. | ||
