Finished

         elif term.is_Add:
             p, q = term.as_numer_denom()
+            # Check for the specific problematic case where we have terms like c + d**(-k)
+            # where c is independent of k but d**(-k) depends on k. This leads to
+            # incorrect factorization where Product(c + d**(-k), k) != Product(c*d**k + 1, k) / Product(d**k, k)
+            if (k in p.free_symbols and k in q.free_symbols and
+                term.is_Add and len(term.args) == 2 and
+                any(arg.is_Pow and k in arg.exp.free_symbols and k not in arg.base.free_symbols for arg in term.args) and
+                any(k not in arg.free_symbols for arg in term.args)):
+                # This is the problematic case like n + 1/2**k where n is independent of k
+                return None
             q = self._eval_product(q, (k, a, n))
             if q.is_Number:

trust