chapter  26
Series of Functions
ByRavi P. Agarwal, Peter Cristina, O’Regan Donal
Pages 8

Just as the convergence of a series of numbers is defined in Chapter 9 to mean the convergence of the sequence of partial sums, the convergence of a series of functions is also defined in terms of the sequence of partial sums. Thus, every result established in Chapters 24 and 25 for sequences of functions can be directly extended for series of functions.