1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
  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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook