A real series is a mathematical concept that involves the sum of a sequence of real numbers. It is typically expressed in the form S = a_1 + a_2 + a_3 + \ldots , where each a_n is a real number. The series can converge, meaning it approaches a specific value, or diverge, meaning it does not settle at any particular value. In calculus, the study of real series is important for understanding functions and their behaviors. The convergence of a series can be analyzed using various tests, such as the Ratio Test or the Root Test. These tools help mathematicians determine whether a series will yield a finite sum.