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1Aug/114

A nice proof without words

Here's a very cool proof without words by Burkard and Marty.


Can you figure out what this proof without words illustrates?

Comments (4) Trackbacks (1)
  1. this is basically the result found by a Bernoulli (I don’t remember which one), right?

  2. That \sum_{x=1}^{\infty} 1/x^k converges for any k >= 2 and is < 1

    It doesn't provide what it converges to though.

    What's interesting is I wonder if this idea could be extended to show that harmonic series don't converge.

  3. In a way, it’s cheating a little in that it sort of assumes 1/2 + 1/4 + 1/8 + … = 1, so all the columns actually do fit into the square. But I think you can kind of see they do fit in the square.
    I guess you could deduce from it (Pi^2)/6-1<1 so Pi<3.47

  4. (1/2^2)+(1/3^2)+(1/4^2)+(1/5^2)+(1/6^2)+…… < 1


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