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I would like to expand the following expression:

1/[((a+s)*(1+b/s)^m)], where a, b, and s are real nonnegative values and m is an arbitrary positive integer.

Particularly, according to partial fraction expansion, it becomes:

Sum[A_j/[(1+b/s)^j],{j,1,m}]+B/(a+s). I look for a closed-form expression of A_j and B.

Any help could be useful.

Thank you in advance.