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

Henry Anorue

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
common_ratio =splitted_float / 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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geometric series
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python
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Henry Anorue
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