Summations

See book section

Mathematical Concept of Summations:

In mathematics, summation is a concept that represents the addition of a sequence of numbers or terms. It is denoted by the symbol “Σ” (sigma) and is used to express the total sum of a series of terms. The general form of a summation is:

\(\sum_{n=1}^{k} f(n)\)

Here, \(n\) is the index variable that takes on values from 1 to \(k\) and \(f(n)\) is the function that defines the terms to be summed. The summation symbol indicates that we need to add up all the terms in the series for each value of \(n\).

Example of Summation:

Let’s consider the following example of a simple summation:

\(\sum_{n=1}^{5} n\)

This summation represents adding up all the integers from 1 to 5:

1 + 2 + 3 + 4 + 5 = 15

Implementing Summations in Python:

In Python, you can use loops to implement summations. The for loop is commonly used to iterate through a range of values and accumulate the sum.

Example of Summation in Python:

Code

# Calculate the summation Σ (n = 1 to 5) n
total_sum = 0
for n in range(1, 6):
    total_sum += n

print(total_sum)  # Output: 15

15