code: 
  
  from __future__ import annotations
  
  
  
  
  def 				a__	(	lowerCAmelCase ,  lowerCAmelCase ,  lowerCAmelCase ,  )  ->   list[float | int]:
        if not all((nth_term, start_term_a, common_ratio_r)						):
              return []
        UpperCAmelCase__ :       list[float | int]						=						[]
        UpperCAmelCase__ :       int						=						1
        UpperCAmelCase__ :       int						=						common_ratio_r
        for _ in range(int(lowerCAmelCase						)						):
              if not series:
                    series.append(lowerCAmelCase						)
              else:
                    power += 1
                    series.append(float(start_term_a * multiple						)						)
                    UpperCAmelCase__ :       Dict						=						pow(float(lowerCAmelCase						) ,  lowerCAmelCase						)
        return series
  
  
  if __name__ == "__main__":
      import doctest
  
      doctest.testmod()
  
      _A						=     float(input("""Enter the last number (n term) of the Geometric Series"""))
      _A						=     float(input("""Enter the starting term (a) of the Geometric Series"""))
      _A						=     float(
          input("""Enter the common ratio between two terms (r) of the Geometric Series""")
      )
      print("""Formula of Geometric Series => a + ar + ar^2 ... +ar^n""")
      print(geometric_series(nth_term, start_term_a, common_ratio_r))
  
  
style_context: 
  
  """simple docstring"""
  from __future__ import annotations
  
  
  
  
  def 				a__	(	lowerCAmelCase						)  ->   set[int]:
        UpperCAmelCase__ :       List[Any]						=						{1}
        UpperCAmelCase__ :       Optional[int]						=						[1]
        for _ in range(2 ,  depth + 1						):
              UpperCAmelCase__ :       Tuple						=						[*previous_coefficients, 0]
              UpperCAmelCase__ :       List[str]						=						[0, *previous_coefficients]
              UpperCAmelCase__ :       Dict						=						[]
              for x, y in zip(lowerCAmelCase ,  lowerCAmelCase						):
                    coefficients.add(x + y						)
                    previous_coefficients.append(x + y						)
        return coefficients
  
  
  
  
  def 				a__	(	lowerCAmelCase						)  ->   set[int]:
        UpperCAmelCase__ :       List[str]						=						set()
        for number in unique_coefficients:
              UpperCAmelCase__ :       int						=						2
              UpperCAmelCase__ :       List[Any]						=						number
              while divisor**2 <= copy_number:
                    UpperCAmelCase__ :       Tuple						=						0
                    while copy_number % divisor == 0:
                          copy_number //= divisor
                          multiplicity += 1
                    if multiplicity >= 2:
                          non_squarefrees.add(lowerCAmelCase						)
                          break
                    divisor += 1
  
        return unique_coefficients.difference(lowerCAmelCase						)
  
  
  
  
  def 				a__	(	lowerCAmelCase = 51						)  ->   int:
        UpperCAmelCase__ :       Any						=						get_pascal_triangle_unique_coefficients(lowerCAmelCase						)
        UpperCAmelCase__ :       Dict						=						get_squarefrees(lowerCAmelCase						)
        return sum(lowerCAmelCase						)
  
  
  if __name__ == "__main__":
      print(f'''{solution() = }''')
  
  