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2(5!) − cot [4 arctan 0.2 + (i/2) ln i] − 1

  1. Jan 20, 2016 #1
    Don't ever divide anything by the quantity in the title.

    Post your favorite "fancy zeros" here.
     
  2. jcsd
  3. Jan 21, 2016 #2
    $$\frac{1}{12} + \sum _{n = 1} ^\infty n$$
     
  4. Jan 23, 2016 #3
    That should probably be

    −1/12 + Σ(2,∞) 1/n⁴

    Edit: whoops, no. That doesn't seem quite right, either. I evaluated ten million terms of the sum and came up with −0.0010100996222299347, so

    −1/12 + 1/999 + Σ(2,∞) 1/n⁴

    seems to be nearer to zero.
     
    Last edited: Jan 23, 2016
  5. Jan 23, 2016 #4
    Nope, it's written as I intended.
     
  6. Jan 23, 2016 #5

    mfb

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    2016 Award

    Staff: Mentor

    Unless you specify how divergent sums are to be evaluated, the formula is not well-defined.
    Yes there is a specific way that leads to -1/12, but this is by far not the only way to assign finite values to divergent sums.
     
  7. Jan 23, 2016 #6
    It was a somewhat tongue-in-cheek answer, if that wasn't clear.
     
  8. Jan 23, 2016 #7
    I tried something like this to mess with my maths teacher in senior year once, replaced pi with some weird sums.
     
  9. Jan 23, 2016 #8
    1 / Σ(1,∞) n = 0
    1 / { 1/a + 1 / Σ(1,∞) n } = a, a≠0.
     
  10. Jan 23, 2016 #9
  11. Jan 23, 2016 #10
    ## \begin{Vmatrix} \vec\nabla \times \vec\nabla f \end{Vmatrix} ##
     
    Last edited: Jan 23, 2016
  12. Jan 24, 2016 #11
    Ah. My difficulty in appreciating the assignment was caused by my thinking of scalars in vector terms. Consider velocities in the same direction, classically being added, tail to head:

    v₁ + v₂ + v₃ + v₄ + ...

    where each velocity is in the direction of the +x axis and the magnitude of the velocities is proportional to the subscript.

    How is it that an object, moving through an infinite succession of changes-of-velocity, all of them forward, might end up moving BACKWARD at a speed of 1/12 velocity units?

    I'd figured that this was a case of getting a strange result out of an indeterminate form.
     
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