Taylor series represent analytic functions as infinite sums with only non-negative powers of a variable, while Laurent series represent functions that may have singularities by including both positive and negative powers of the variable. The choice between them depends on whether the function is analytic at the point of expansion; Taylor series are for analytic points, and Laurent series are for points where the function is not analytic but is analytic in a neighborhood. MJC - 04 Paper - V for Bihar University, Muz.