

from math import isclose, sqrt



def   __UpperCAmelCase					(      __a :     float						,__a :     float						,__a :     float      )     ->	tuple[float, float, float]:

					"""simple docstring"""

					_a      :       Any   =						point_y / 4 / point_x
					_a      :       Dict   =						2 * normal_gradient / (1 + normal_gradient * normal_gradient)
					_a      :       Optional[Any]   =						(1 - normal_gradient * normal_gradient) / (
					    1 + normal_gradient * normal_gradient
					)
					_a      :       Optional[Any]   =						(sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

					# to find the next point, solve the simultaeneous equations:
					# y^2 + 4x^2 = 100
					# y - b = m * (x - a)
					# ==> A x^2 + B x + C = 0
					_a      :       List[Any]   =						outgoing_gradient**2 + 4
					_a      :       int   =						2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
					_a      :       Optional[int]   =						(point_y - outgoing_gradient * point_x) ** 2 - 100

					_a      :       List[str]   =						(
					    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term      )
					) / (2 * quadratic_term)
					_a      :       Dict   =						(
					    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term      )
					) / (2 * quadratic_term)

					# two solutions, one of which is our input point
					_a      :       Optional[Any]   =						x_minus if isclose(__a						,__a      ) else x_plus
					_a      :       Optional[Any]   =						point_y + outgoing_gradient * (next_x - point_x)

					return next_x, next_y, outgoing_gradient



def   __UpperCAmelCase					(      __a :     float = 1.4						,__a :     float = -9.6      )     ->	int:

					"""simple docstring"""

					_a      :       int   =						0
					_a      :       float   =						first_x_coord
					_a      :       float   =						first_y_coord
					_a      :       float   =						(10.1 - point_y) / (0.0 - point_x)

					while not (-0.01 <= point_x <= 0.01 and point_y > 0):
										_a ,   _a ,   _a      :       Dict   =						next_point(__a						,__a						,__a      )
										num_reflections += 1

					return num_reflections


if __name__ == "__main__":
			print(f'''{solution() = }''')






def   __UpperCAmelCase					(      __a :     str      )     ->	list:

					"""simple docstring"""

					if n_term == "":
										return []
					_a      :       list   =						[]
					for temp in range(int(__a      )      ):
										series.append(F"""1/{temp + 1}""" if series else '''1'''      )
					return series


if __name__ == "__main__":
			a__												=						input('''Enter the last number (nth term) of the Harmonic Series''')
			print('''Formula of Harmonic Series => 1+1/2+1/3 ..... 1/n''')
			print(harmonic_series(nth_term))



