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A series is a mathematical concept in Calculus that represents the sum of an infinite sequence of numbers or terms. It can be thought of as an infinite sum, where each term is added to the previous term.
The study of series in Calculus is important because it allows us to understand and analyze functions that cannot be easily solved using traditional methods. Series also have many real-world applications, such as in physics, engineering, and finance.
To determine the convergence or divergence of a series, we can use various tests such as the comparison test, ratio test, integral test, or alternating series test. These tests help us determine if the series approaches a finite limit (converges) or goes to infinity (diverges).
A convergent series is one whose sum approaches a finite limit as the number of terms increases, while a divergent series is one whose sum goes to infinity as the number of terms increases. In other words, a convergent series has a finite sum, while a divergent series has an infinite sum.
The sum of a convergent series can be found by using the formula for the sum of an infinite geometric series or by using the partial sum formula. It is also important to note that not all series have a finite sum, and some may require more advanced techniques to find their sum.
