  Sums of the form $\sum_{N_m=q}^{n}{\cdots
\sum_{N_1=q}^{N_2}{a_{(m);N_m}\cdots a_{(1);N_1}}}$ where the $a_{(k);N_k}$'s
are same or distinct sequences appear quite often in mathematics. We will refer
to them as recurrent sums. In this paper, we introduce a variety of formulas to
help manipulate and work with this type of sums. We begin by developing
variation formulas that allow the variation of a recurrent sum of order $m$ to
be expressed in terms of lower order recurrent sums. We then proceed to derive
theorems (which we will call inversion formulas) which show how to interchange
the order of summation in a multitude of ways. Later, we introduce a set of new
partition identities in order to then prove a reduction theorem which permits
the expression of a recurrent sum in terms of a combination of non-recurrent
sums. Finally, we apply this reduction theorem to a recurrent form of two
famous types of sums: The $p$-series and the sum of powers.
