91Ó°ÊÓ

In this exercise, we have the arithmetic series \(\textstyle\sum_{i=1}^{5}(i+3)\)\'. An arithmetic series is a sequence of numbers in which the difference between consecutive terms is constant. The series sum is the total we get when we add all the terms of the series together.
First, we identify the series and generate the terms by replacing \(\textstyle i\)\' with the given range, from 1 to 5 in this case. When you do this, you get the list of numbers: 4, 5, 6, 7, and 8.
The next step is to write the series as a sum of its terms: \(4 + 5 + 6 + 7 + 8\). Finally, add these terms together to find the series sum, which is 30.
Understanding how to sum a series involves grasping the pattern in the sequence and calculating the total. This concept is essential in various fields like finance, computer science, and physics, where summing sequences often comes into play.

Addition is the basic mathematical operation of combining two or more numbers to get a total. In this exercise, we add the terms of the series 4, 5, 6, 7, and 8.
Each addition step builds on the previous one:

• \(4 + 5 = 9\)
• \(9 + 6 = 15\)
• \(15 + 7 = 22\)
• \(22 + 8 = 30\)

By breaking the addition into smaller, manageable parts, it's easier to ensure accuracy.
Addition is a skill we use in everyday life, from totaling expenses to calculating scores, making it foundational for both simple and complex mathematics.

A sequence is an ordered list of numbers that follow a specific pattern. Here, the sequence stems from the series: \(\textstyle (i + 3)\) where \(i\) ranges from 1 to 5.
This sequence becomes: 4, 5, 6, 7, 8. The pattern is straightforward: each term increases by 1 from the previous term.
Recognizing sequences helps in predicting future terms based on previous ones.
Sequences are visible in various real-world scenarios, such as daily temperatures, stock prices, or any data sets collected over time.
Understanding sequences allows for better data analysis and problem-solving, foundational in fields like economics, engineering, and natural sciences.