  There are numerous ways to represent real numbers. We may use, e.g., Cauchy
sequences, Dedekind cuts, numerical base-10 expansions, numerical base-2
expansions and continued fractions. If we work with full Turing computability,
all these representations yield the same class of real numbers. If we work with
some restricted notion of computability, e.g., polynomial time computability or
primitive recursiveness, they do not. Irrational numbers can be represented by
infinite sums of certain forms. We prove some results related to representation
of irrational numbers by infinite sums.
