


'''simple docstring'''

def __snake_case      (   UpperCAmelCase_		:		str	):
 assert isinstance(UpperCamelCase__      ,       UpperCamelCase__	), F'''The input value of [n={number}] is not an integer'''

 if number == 1:
  return 2
 elif number < 1:
  lowerCamelCase_  				=						F'''The input value of [n={number}] has to be > 0'''
  raise ValueError(UpperCamelCase__	)
 else:
  lowerCamelCase_  				=						sylvester(number - 1	)
  lowerCamelCase_  				=						num - 1
  lowerCamelCase_  				=						num
  return lower * upper + 1


if __name__ == "__main__":
 print(f'''The 8th number in Sylvester\'s sequence: {sylvester(8)}''')







'''simple docstring'''

import math





def __snake_case      (   UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		float	):
 return math.pow(UpperCAmelCase_      ,       2	) - a





def __snake_case      (   UpperCAmelCase_		:		float	):
 return 2 * x





def __snake_case      (   UpperCAmelCase_		:		float	):
 lowerCamelCase_  				=						2.0

 while start <= a:
  lowerCamelCase_  				=						math.pow(UpperCAmelCase_      ,       2	)

 return start





def __snake_case      (   UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		int = 9999      ,       UpperCAmelCase_		:		float = 0.00_0000_0000_0001	):

 if a < 0:
  raise ValueError("math domain error"	)

 lowerCamelCase_  				=						get_initial_point(UpperCAmelCase_	)

 for _ in range(UpperCAmelCase_	):
  lowerCamelCase_  				=						value
  lowerCamelCase_  				=						value - fx(UpperCAmelCase_      ,       UpperCAmelCase_	) / fx_derivative(UpperCAmelCase_	)
  if abs(prev_value - value	) < tolerance:
   return value

 return value


if __name__ == "__main__":
     from doctest import testmod

     testmod()



