Let (b1, b2, …) be an infinite sequence of real numbers. The sum  is defined by induction...

Let (b1, b2, …) be an infinite sequence of real numbers. The sum  is defined by induction as follows:

Let A be the set of real numbers; choose ρ so that Theorem 8.4 applies to define this sum rigorously. We sometimes denote the sum  by the symbol b1 + b2 + ⋯ + bn.