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A series is a sum of an infinite sequence of numbers. It can be written as ∑an, where a is the terms of the sequence and n is the index of the terms.
An integral is a mathematical concept that represents the area under a curve. It is often used to calculate the total value or quantity of a function over a given interval.
To investigate convergence of a series, you can use various tests such as the comparison test, ratio test, or integral test. These tests can help determine whether a series converges or diverges.
Absolute convergence refers to a series where the sum of the absolute values of the terms converges. Conditional convergence, on the other hand, refers to a series where the sum of the terms converges, but not the absolute values of the terms.
Investigating convergence of a series is important because it allows us to determine whether the sum of an infinite sequence of numbers will converge to a finite value or diverge to infinity. This information is crucial in many applications of mathematics and science.