Problem 79 - College Algebra

Question

What is the meaning of the symbol \(\Sigma ?\) Give an example with your description.

Step-by-Step Solution

Answer

The Greek symbol \(\Sigma\) represents a summation, that is the addition of a sequence of numbers. For example, \(\Sigma^{5}_{i=1} i\) calculates the sum of all integers from 1 to 5, which equals 15.

Step 1: Understanding the Sigma Symbol

The Greek symbol \(\Sigma\) is mostly used to represent 'sum' or 'summation'. It is a method by which a series of entities can be summed up. It's often found in mathematics, specifically in arithmetic and calculus.

Step 2: Usage of the Sigma Symbol

When using the sigma symbol \(\Sigma\), we generally state the variable used for the summation, the lower limit (where the summation starts), and the upper limit (where the summation ends). The expression of which the summation occurs is written to the right of the sigma. For example, \(\Sigma^{n}_{i=1} i\) points to the sum of all integers from 1 to n.

Step 3: Giving an Example

Let's use the given example \(\Sigma^{5}_{i=1} i\). This means we are summing all integers i from 1 to 5. So, the calculation is as follows: \(1+2+3+4+5=15\).