6

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.

**6.1 Series**

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 ...

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