what is the difference between finite and infinite sequence?
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A finite sequence has a starting number, a difference or factor, and a fixed total number of terms. ... Infinite sequences don't have a fixed number of terms, and their terms can grow to infinity, decrease to zero or approach a fixed value. The corresponding series can also have an infinite, zero or fixed result.
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What is the difference between a sequence and a series? The list of numbers written in a definite order is called a sequence. The sum of terms of an infinite sequence is called an infinite series. ... Therefore sequence is an ordered list of numbers and series is the sum of a list of numbers.
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As we know that if a set has a starting point and an ending point both, it is a finite set, but it is infinite if it has no end from any side or both sides. ... If a set has the unlimited number of elements then it is infinite and if the elements are countable then it is finite.
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There is a key difference between sequence and chronological: texts organized chronologically occur at a specific time and setting, whereas texts describing sequences do not occur at any specific time and place.
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Note: it is true that every bounded sequence contains a convergent subsequence, and furthermore, every monotonic sequence converges if and only if it is bounded. Added See the entry on the Monotone Convergence Theorem for more information on the guaranteed convergence of bounded monotone sequences.
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The key difference between similarity and identity in sequence alignment is that similarity is the likeness (resemblance) between two sequences in comparison while identity is the number of characters that match exactly between two different sequences.
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Topic 4. The differences between arithmetic and geometric sequences is that arithmetic sequences follow terms by adding, while geometric sequences follow terms by multiplying. The similarities between arithmetic and geometric sequences is that they both follow a certain term pattern that can't be broken.
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To prove that a sequence is divergent one must show that that the sequence does not approach a finite limit as the number of terms in the sequence increases toward infinity. Intuitively (-1)n is divergent, as it switches between 1 for each even value of n and -1 for each odd value of n.
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There is a stark difference between Infinite and not defined number . Any number when divided by zero is a not defined number whereas infinite are vague large number that is dependent on reference or reader . For example - when you divide 5 by 0.1 , then ans. is 5 .
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The difference between Indefinite and Unlimited When used as adjectives, indefinite means without limit, whereas unlimited means limitless or without bounds.
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A discrete variable has a complete range of values. ... A continuous variable is uncountable while a discrete variable has countable values. The data set for a discrete variable is finite meaning it has an end value while a continuous variable can take up an infinite value which implies that it can have endless values.
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Clearly every finite set is countable, but also some infinite sets are countable. Note that some places define countable as infinite and the above definition. In such cases we say that finite sets are "at most countable". We say that a set A is uncountable if and only if it is not countable.
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When we say in calculus that something is "infinite," we simply mean that there is no limit to its values. ... We say that as x approaches 0, the limit of f(x) is infinity. Now a limit is a number. So when we say that the limit of f(x) is infinity, we mean there is no limit to its values.
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An arithmetic sequence is a sequence with the difference between two consecutive terms constant. ... A geometric sequenceis a sequence with the ratio between two consecutive terms constant.
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Theorem: The set of all finite-length sequences of natural numbers is countable. This set is the union of the length-1 sequences, the length-2 sequences, the length-3 sequences, each of which is a countable set (finite Cartesian product).
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A series can converge or diverge. A series that converges has a finite limit, that is a number that is approached. A series that diverges means either the partial sums have no limit or approach infinity. The difference is in the size of the common ratio.
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A sequence is a set of numbers, called terms, arranged in some particular order. An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference. A geometric sequence is a sequence with the ratio between two consecutive terms constant.