  Srinivasa Ramanujan provided Fourier series expansions of certain
arithmetical functions in terms of the exponential sum defined by
$c_q(n)=\sum\limits_{\substack{{m=1}\\(m,q)=1}}^{q}e^{\frac{2 \pi imn}{q}}$.
Later, H. Delange derived the bound $\sum\limits_{q|k}|c_q(n)|\leq n\,
2^{\omega(k)}$ and gave a sufficient condition for such expansions to exist. A.
Grytczuk gave an exact value for this bound, and derived a converse implication
of the absolute convergence stated by H. Delange. We here show that these
results have natural generalizations in terms of the Cohen-Ramanujan sum
$c_q^{(s)}(n)$ defined by E. Cohen in [\emph{Duke Mathematical Journal,
16(85-90):2, 1949}]. We derive a bound as well as exact value for
$\sum\limits_{q|k}|c_q^{(s)}(n)|$ and provide a sufficient condition for the
Cohen-Ramanujan expansions to exist.
