Application Of Residue Theorem In Summation Of Certain Class Of Series:- Sabastine, Victor C

ABSTRACT This project presents the application ofthe residue theorem in the summation of certain classes of series. The residue is a fundamental tool in complex analysis that allows for the evaluation of contour integrals around simple closed curves. By applying the residue theorem, we can use certain trigonometric function to obtain the summation ofspecific series, such as the sum ofthe reciprocals ofthe natural numbers or the sum ofthe reciprocal ofthe natural number raised to power four. The results obtained provide a deeper understanding ofthe properties ofthese series and have important implications in various fields, including mathematics, physics and computer science. The project demonstrates the power and versatility of the residue theorem in evaluating complex problems involving series.