摘要
Here is introduced some novel algorithms which made use of polygarnma functions to get the exact limits of a broad class of infinite series. Moreover, Laplace transform is used to find the sum of many convergent infinite series. These exact limits are found in different branches of physics for some special cases series and are in complete agreement with the values found by other authors. Moreover, the methods presented here are generalized and applied to other wide variety of sums, including alternating series. Finally, these methods are simple and quite powerful to calculate the limits of many convergent series as you can see from the examples included.
