




from math import isclose, sqrt







def      lowerCamelCase_						(			UpperCamelCase__							: float					,	UpperCamelCase__							: float					,	UpperCamelCase__							: float )	->			tuple[float, float, float]:





				"""simple docstring"""


				__lowerCamelCase									=       point_y / 4 / point_x
				__lowerCamelCase									=       2 * normal_gradient / (1 + normal_gradient * normal_gradient)
				__lowerCamelCase									=       (1 - normal_gradient * normal_gradient) / (
				    1 + normal_gradient * normal_gradient
				)
				__lowerCamelCase									=       (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
				__lowerCamelCase									=       outgoing_gradient**2 + 4
				__lowerCamelCase									=       2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
				__lowerCamelCase									=       (point_y - outgoing_gradient * point_x) ** 2 - 100

				__lowerCamelCase									=       (
				    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term )
				) / (2 * quadratic_term)
				__lowerCamelCase									=       (
				    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term )
				) / (2 * quadratic_term)

				# two solutions, one of which is our input point
				__lowerCamelCase									=       x_minus if isclose(UpperCamelCase__					,	UpperCamelCase__ ) else x_plus
				__lowerCamelCase									=       point_y + outgoing_gradient * (next_x - point_x)

				return next_x, next_y, outgoing_gradient







def      lowerCamelCase_						(			UpperCamelCase__							: float = 1.4					,	UpperCamelCase__							: float = -9.6 )	->			int:





				"""simple docstring"""


				__lowerCamelCase									=       0
				__lowerCamelCase									=       first_x_coord
				__lowerCamelCase									=       first_y_coord
				__lowerCamelCase									=       (10.1 - point_y) / (0.0 - point_x)

				while not (-0.01 <= point_x <= 0.01 and point_y > 0):
								__lowerCamelCase			,		__lowerCamelCase			,		__lowerCamelCase									=       next_point(UpperCamelCase__					,	UpperCamelCase__					,	UpperCamelCase__ )
								num_reflections += 1

				return num_reflections


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








def      lowerCamelCase_						(			UpperCamelCase__							: str )	->			list:





				"""simple docstring"""


				if n_term == "":
								return []
				__lowerCamelCase									=       []
				for temp in range(int(UpperCamelCase__ ) ):
								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))


