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  1. Limit[Sum[1/((2 n + 1) Pi I - x), {n, -m, m}], m -> ∞]
  2. = -(1/2) Tanh[x/2]
  3.  
  4. Sum[1/((2 n + 1) Pi I - x), {n, -∞, ∞}]
  5. Sum::div: Sum does not converge.
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