Elements that comprise a sequence, series, or equation are known as terms, of which there may be a finite or infinite number. Negligible terms are those terms in a sequence, series, or equation that can be largely ignored, primarily because they hold such small values as to not affect the end result in a meaningful way. Thus, they are termed negligible, or umimportant, in relation to the task at hand. Use of the concept of negligible terms is found whenever one uses numerical methods to approximate a solution. It is applied frequently in applied and computational mathematics.

Most commonly, negligible terms are discarded when one is attempting to approximate a value within a specified error. The specified error may represent either a finite number--such as approximating pi within 1/1000th of its actual value--or an order of magnitude, such as using a Taylor series to approximate sin...