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  1. import math
  2.  
  3. def continued_fraction_sqrt2(iterations=100):
  4. 	x = 0
  5. 	for _ in range(iterations):
  6. 		x = 1 / (2 + x)
  7. 		result = 1 + x
  8. 		return result
  9. iterations = 100
  10. approx = continued_fraction_sqrt2(iterations)
  11. print(f"Approximation of sqrt(2) after {iterations} iterations: {approx:.15f}")
  12. print(f"math.sqrt(2) = {math.sqrt(2):.15f}")
  13. print(f"Differece = {abs(math.sqrt(2) - approx):.15f}")
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Approximation of sqrt(2) after 100 iterations: 1.500000000000000
math.sqrt(2) = 1.414213562373095
Differece = 0.085786437626905


	

		
	 
	
	
			

					
			
			
			
			
			
			
			
			

			
			
			
		

	
		
		

			

			                        







			
			

				

	
					
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Python 3 (python  3.12)

					

					

						
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11 days ago

					

					

						
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