Sigma Notation: A Concise Mathematical Notation for Summing Series

Sigma Notation

Sigma notation, denoted by the Greek letter sigma (Σ), is a mathematical notation used to represent the sum of a series

Sigma notation, denoted by the Greek letter sigma (Σ), is a mathematical notation used to represent the sum of a series. It provides a concise way to write a sequence of terms that follow a pattern. Sigma notation is commonly used in various branches of mathematics, including calculus, statistics, and discrete mathematics.

The general format of sigma notation is:

Σ(n = a to b) f(n)

Here, “n = a to b” represents the range of values that the variable ‘n’ takes. ‘a’ denotes the starting value of ‘n’, and ‘b’ represents the ending value. The expression ‘f(n)’ represents the function or formula that generates the terms of the series.

To evaluate a sigma notation, you replace ‘n’ with each value within the given range and calculate the corresponding terms. Then, you add all these terms together to obtain the sum of the series.

Let’s look at an example to illustrate how to work with sigma notation. Suppose we have the following series:

Σ(k = 1 to 5) 2k

To evaluate this series, we replace ‘k’ with each value from 1 to 5 and calculate the terms:

When k = 1, 2k = 2(1) = 2
When k = 2, 2k = 2(2) = 4
When k = 3, 2k = 2(3) = 6
When k = 4, 2k = 2(4) = 8
When k = 5, 2k = 2(5) = 10

Now, we add all these terms together:

2 + 4 + 6 + 8 + 10 = 30

Hence, the sum of the series Σ(k = 1 to 5) 2k is 30.

Sigma notation is helpful in simplifying and representing long series in a compact form. It allows for easier computation and analysis of series, especially when working with large sets of numbers or patterns with complex formulas.

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