infinite series

• How Do You Differentiate a Double Summation?
  Differentiate finite double sums term by term; for infinite sums, check uniform convergence of the derivative series before interchanging differentiation and summation.
• How Do Limits Resolve Zeno’s Achilles Paradox?
  Zeno’s Achilles paradox is resolved mathematically by showing that infinitely many shrinking time intervals sum to a finite limit, when motion is modeled continuously.