Main Question or Discussion Point
Just to be clear, I understand the difference between sigma summation and integration. Sigma summation is, put simply, the discrete version of integration. Rather than a continuous sum of a function for given values, sigma summation provides a sum of a function for given regions that is evaluated at discrete intervals. My question is: When would sigma summation ever be used as a more effective substitute for integration? Integration can only be more accurate than sigma summation as a result of its infinitely continuous nature...right? When -- in the world of physics -- is discrete summation a more accurate means of evaluating the sum for given values of a function?