  For any integer $q\geq 2$ we provide a formula to express indefinite sums of
a sequence $(f(n))_{n\geq 0}$ weighted by $q$-periodic sequences in terms of
indefinite sums of sequences $(f(qn+p))_{n\geq 0}$, where
$p\in\{0,\ldots,q-1\}$. When explicit expressions for the latter sums are
available, this formula immediately provides explicit expressions for the
former sums. We also illustrate this formula through some examples.
