 As a third equivalent characterization, it is an infinite sequence of the form

formula_1

where "a" is not zero and −"a"/"d" is not a natural number, or a finite sequence of the form

formula_2

where "a" is not zero, "k" is a natural number and −"a"/"d" is not a natural number or is greater than "k".Infinite harmonic progressions are not summable (sum to infinity).It is not possible for a harmonic progression of distinct unit fractions (other than the trivial case where "a" = 1 and "k" = 0) to sum to an integer.