Many of the functions which are encountered in mathematical applications are represented by an infinite series. The sum of an infinite series may or may not exist.

For example, the sum of the infinite geometric series is equal to 2, whereas the sum of the infinite geometric series 1 + 2 + 4 + 8 + … ∞ is ∞, which is not a real number and so the sum does not exist. The usage of an infinite series, whose sum does not exist, will lead to absurd conclusions in scientific investigations. Thus, an infinite series must be tested for the existence of its sum. This aspect is the study of convergence of the infinite ...

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