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We consider the central configurations of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mi>N</mi></mrow></semantics></math></inline-formula>-body problem, where <i>N</i> bodies are infinitesimal and the remaining one body is dominant. For regular polygon central configurations, we prove that the masses of all the infinitesimal bodies are equal when <i>N</i> is odd and the masses of the alternate infinitesimal bodies must be equal when <i>N</i> is even. Moreover, in the case of <i>N</i> being even, we present the relationship of the mass parameters between two consecutive infinitesimal bodies.