Series and limits
Many examples exist in the physical sciences of situations where we are presented with a sum of terms to evaluate. As just two examples, there may be the need to add together the contributions from successive slits in a diffraction grating in order to find the total light intensity at a particular point, or to compute, for a particular site in a crystal, the electrostatic potential due to all the other ions in the crystal.
A general series may have either a finite or infinite number of terms. In either case, the sum of the first N terms of a series (often called a partial sum) is written
where the terms of the series ...