Write a Python program that implements the Taylor series expansion of the function In(1+x) for any...

 

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• Write a Python program that implements the Taylor series expansion of the function In(1+x) for any x in the interval (-1,1], as given by: In(1 + x) = x -+-+-.... • The program should prompt the user to enter the number of terms n. If n > 0, the program prompts the user to enter the value of x. If the value of x is in the interval (-1, 1], the program calculates the approximation to ln(1 + x) using the first n terms of the above series. • The program displays the approximate value as well as the actual value calculated using the standard log function. • Note that the program should validate the user input for different values. If an invalid value is entered, the program should outputs an appropriate error messages and loops as long as the input is not valid. Sample program run: Enter number of terms: 0 Error: Zero or negative number of terms not accepted Enter the number of terms: 9000 Enter the value of x in the interval (-1, 1]: -2 Error: Invalid value for x Enter the value of x in the interval (-1, 1]: 0.5 The approximate value of In(1+0.5000) up to 9000 terms is 0.4054651081 and the value using the standard log function is 0.4054651081 • Note that your program should be general and work if we change the values of the input. Activate Wi • Write a Python program that implements the Taylor series expansion of the function In(1+x) for any x in the interval (-1,1], as given by: In(1 + x) = x -+-+-.... • The program should prompt the user to enter the number of terms n. If n > 0, the program prompts the user to enter the value of x. If the value of x is in the interval (-1, 1], the program calculates the approximation to ln(1 + x) using the first n terms of the above series. • The program displays the approximate value as well as the actual value calculated using the standard log function. • Note that the program should validate the user input for different values. If an invalid value is entered, the program should outputs an appropriate error messages and loops as long as the input is not valid. Sample program run: Enter number of terms: 0 Error: Zero or negative number of terms not accepted Enter the number of terms: 9000 Enter the value of x in the interval (-1, 1]: -2 Error: Invalid value for x Enter the value of x in the interval (-1, 1]: 0.5 The approximate value of In(1+0.5000) up to 9000 terms is 0.4054651081 and the value using the standard log function is 0.4054651081 • Note that your program should be general and work if we change the values of the input. Activate Wi

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