How to compute the sum of 1 + 1⁄2 + 1⁄4 + ... + 1/2n

Below is an algorithm that uses the Python programming language to calculate the sum of 1 + 1/2 + 1/4 +... + 1 / 2n.

Methodology

  • Import a Python class called Fraction from the fraction module.

  • Then, create a function called sum_of_series that takes a string as an argument; in this case, the series or the sum of numbers.

  • Next, split the string into a list and convert all items in the list to float.

  • Solve for first_term and common_ratio of the series, and then number_of_terms.

  • Finally, generate a general formula for the series called result. This result is equal to the numerator divided by the denominator.

Code

        
from fractions import Fraction 
def sum_of_series(string): 
    # splitted the string into a list
    # replaced the extra spaces with no spaces and 
    # converted all elements in the list into float
    splitted = string.replace(' ','').split("+")
    splitted_float = []
    for item in splitted:
        splitted_float.append(float(Fraction(item)))
        
    # getting first term using the index of the splitted_float
    first_term = splitted_float[0]
    common_ratio =splitted_float[1] / first_term
    number_of_terms = float(len(splitted_float))
    # created a general formula for the series called result.
    # result is equal to numerator/denominator 
    numerator = first_term * ( 1 - (common_ratio**number_of_terms))
    denominator = (1 - common_ratio)
    result = numerator / denominator
    return result
print((sum_of_series("1 + 1/2 + 1/4 + 1/8 ")))

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