Ramanujan's Formula for π

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He was such an oddity. All of the earlier formulas for calculating π involved mostly simple numbers. But look at Ramanujan's:

\frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum^\infty_{k=0} \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}}

It makes sense that someone who instantly could see what a special number 1729 is could come up with a formula like the above.

Comments

  1. Pedro5:28 PM

    I think he has several of those, and I think I've read somewhere that they all seem to be right, but in some cases no one has been able to actually prove they are right.

    Now that's a real genius.

    ReplyDelete

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