3
$\begingroup$

Given that $μ$ and $Q$ are real constants and $i$ is a positive integer, evaluate

$$\sum_{i=1}^{+\infty}\;i\,\tan^{-1}\left(\frac{\mu Q}{\mu^2+\left(i^2-\frac{1}{4}\right)Q^2}\right)$$

  • 1
    Minor points: it's potentially confusing to use $i$ as a variable when it could also be the imaginary unit, and it's not simply "a" positive integer, because it runs over an infinite number of values.2011-10-23
  • 0
    @anon: Sorry! "i" runs over an infinite number of values and NOT imaginary unit2011-10-23
  • 0
    Hmm. Try and find where it might converge. It seems to only do so when $\mu$ or $Q$ is zero.2011-10-23

2 Answers 2