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Series sum

  1. Feb 28, 2012 #1
    what is the sum of the following series? I know it's convergent (using ratio test) but I'm not able to work it out :(
    S=t^(-1) + t^(-4)+t^(-9)............t^(k^2)......to ∞
    where t>1
    Thanks
     
  2. jcsd
  3. Feb 28, 2012 #2
    S = [θ3(1/t)-1]/2, where θ3 is a Jacobi theta function. I strongly suspect S is transcendental for integer t, but couldnt easily find a good reference, nor a convincing argument.
     
  4. Mar 17, 2012 #3
    Hey everyone
    Im a maths tutor and this question was given to one of my students. i may be thinking about it to cryptically so i thought id post it

    5,9,13 ,27,,,217

    i have posted it to various other pupils but no one has gotten it yet.
     
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