Here's a neat visualization.
Note that each color stacks up to make a square of dimension 1x1x1, 2x2x2, 3x3x3, ..etc.pic.twitter.com/zqS0A6fxH3
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The image is not mine, and I can't seem to find the source. If any of you can find it let me know!
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@fergleiser asked: "Is there an integral version of this?" So here's what I came up with. In short, there is!pic.twitter.com/EZdxTxWHDo
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Moreover, it's quite straightforward to do the more general case. Try it out!pic.twitter.com/EWEPAJlG9p
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Note that the general case holds for all n≠-1.
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Yes, but this is induction, which is not very instructive. A much more powerful approach is expansion in lowering factorials, after which you can basically "integrate" sums. See Ch2 of "Concrete Mathematics" by Knuth, Graham and Patashnik for details.pic.twitter.com/SPOThPnSwo
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Thank you so much! Haven't looked into this since I did my degree. Really enjoyed my breakfast!pic.twitter.com/uTVdURtlYE
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Great to hear!
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Is it possible to construct something similar but with integrals?
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Nice question.. I’ll think about that
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