Physics: Sequences and series are used in physics to model various physical phenomena, such as the motion of objects and the behavior of waves.Finance: In finance, sequences, and series are used to calculate compound interest and annuities, which are important for investments and loans.Sequences and Series have numerous practical applications in various fields, including: These are the main the difference between sequence and series. It is used to calculate sums and solve problems in various fields such as finance, physics, engineering, and computer science.Įxample (odd numbers sequence)Įxample ∑(n^2) (sum of squares series), ∑(1/2^n) (geometric series) It is Used to describe patterns and mathematical structures. Here we have the Difference between sequence and series: SequenceĪn ordered list of numbers, objects, or events that follow a specific pattern or rule.ĭisplays the individual terms in a specific order.ĭisplays the sum of the individual terms. The study of convergent and divergent series is important in many areas of mathematics and physics, such as calculus, number theory, and quantum mechanics. A convergent series is one whose sum approaches a finite value as the number of terms increases, while a divergent series is one whose sum approaches infinity or negative infinity as the number of terms increases. Series can be classified as convergent or divergent. Therefore, the sum of the series 1 + 1/2 + 1/4 + 1/8 + … is 2. In this case, the first term is 1, and the common ratio is 1/2, so the sum of the series is: S = 1 / (1 - 1/2) = 2 The sum of an infinite geometric series with a common ratio between -1 and 1 can be calculated using the formula S = a/(1-r), where S is the sum of the series, a is the first term, and r is the common ratio. Series is commonly used in calculus and mathematical analysis to study the behavior of functions and to solve problems involving infinite sums.įor example, consider the series 1 + 1/2 + 1/4 + 1/8 + … This is a geometric series with a common ratio of 1/2. That is, a series is a result of adding up the elements of a sequence, usually denoted by the symbol sigma (Σ). What is a Series?Ī series is the sum of the terms of a sequence. They are also used in computer science to model data structures and algorithms, such as lists, arrays, and linked lists. Sequences play an important role in many areas of mathematics, including calculus, number theory, and combinatorics. Infinite sequences can be described by a formula, such as the Fibonacci sequence, which starts with 0, 1 and each subsequent element is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … A finite sequence has a fixed number of elements, while an infinite sequence continues indefinitely. The elements of a sequence are arranged in a specific order, and each element can be identified by its position in the sequence.įor example, the sequence of even numbers can be written as follows: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, … In this sequence, each element is obtained by adding 2 to the previous element. What is a Sequence?Ī sequence is a set of numbers or other objects that are arranged in a particular order, usually based on a pattern or rule. They also have practical applications in various fields, including engineering, physics, and computer science. Sequences and series help us to understand patterns, relationships, and mathematical structures. In mathematics, a sequence, and a series are two related concepts that are often used in various branches of mathematics, including calculus, number theory, and algebra.
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