Sums of Series

Sums of series involve adding a sequence of numbers together. For example, if you have numbers like 1, 2, 3, and 4, their sum is 10. Some series follow specific patterns, such as adding consecutive numbers or multiplying by a common ratio (geometric series). Mathematicians develop formulas to quickly find the total without adding each term individually, especially for infinite or very long series. Understanding sums of series helps in solving problems across various fields, including economics, engineering, and science, by efficiently calculating totals or predicting behaviors of repeating patterns.