We report a systematic high-resolution angle-resolved photoemission spectroscopy on high-T(c) superconductors Bi(2)Sr(2)Ca(n-1)Cu(n)O(2n+4) (n=1-3) to study the origin of many-body interactions responsible for superconductivity. For n=2 and 3, a sudden change in the energy dispersion, so called "kink", becomes pronounced on approaching (pi,0) in the superconducting state, while a kink appears only around the nodal direction in the normal state. For n=1, the kink shows no significant temperature dependence even across T(c). This could suggest that the coupling of electrons with Q=(pi,pi) magnetic mode is dominant in the superconducting state for multilayered cuprates, while the interactions at the normal state and that of single-layered cuprates have a different origin.