How to compute the harmonic series in Python

Harmonic series is an inverse of arithmetic series. So, if $1/a, 1/(a + d), 1/(a + 2d), 1/(a + 3d) …. 1/(a + nd)$ are in harmonic series then $a, a+d, a+2d, a+3d … a+nd$ will be an arithmetic series

Let's take a look at an example.

Example

Here, we will calculate the sum of the first n numbers in the harmonic series. The sum of the harmonic series will be in the form of:

It can be computed in code as follows:

Code explanation

In the code snippet above:

• Line 2: We declare and define a function calculate_harmonic_sum which takes the number n as a parameter and returns the sum of harmonic series until n.

• Line 3: We declare and assign the variable total_sum which stores the sum of the harmonic series as the series is traversed.

• Lines 4 – 5: We traverse the harmonic series until n using the for loop.

• Line 6: The for loop is executed, returning the sum of the harmonic series total_sum.

• Lines 9 – 10: The print statements call the function calculate_harmonic_sum and pass 7 and 10 as parameters, displaying the sum of their harmonic series.