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<正>When the series have been known to be convergent or divergent,and we want to determine whether the new series converges or diverges.At this situation,we can use the comparison tests to compare a given series with a series that is known.For example:When we see the new series  相似文献   

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Don M. Chance 《CHANCE》2009,22(2):33-42
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The national school-leaving examination in mathematics in England and Wales includes both formal timed written examinations, and a school-based component. Although originally conceived in quite broad terms, the school-based component has been operationalised in terms of quite a narrow range of problems, typically combinatoric in nature, and generally called ‘investigations’. The marking guides given to teachers for the assessment of these problems are generic, in that they are meant to apply to all such problems. In this article it is argued that generic marking guides are unlikely to be successful, and that teachers engaged in assessing school-based work need to take into account features of the specific activity in which the student engages. A corpus of 20,000 student responses to 80 investigative tasks were analyzed to produce a framework of task-factors. The framework characterises tasks in terms of seven factors arranged in four categories. The first category involves the match between the task metaphor and the intended task and the extent to which the task metaphor is likely to be shared by students. The second category concerns the complexity of the task structure, both in terms of the search-space of the task and the relationship between the dependent and independent variables. The third category involves the complexity of the generalisation, both as a term-to-term and as a position-to-term rule. The fourth category is related to whether the kinds of proof required (or possible) are inductive or deductive.  相似文献   

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<正>Series will be introduced briefly in the following paper.It is important in calculus for Newton's idea of representing functions as sums of infinite series.In finding areas,he often integrated a function by expressing it as series.Now,we'll learn infinite sequences.  相似文献   

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<正>Finite sequences and series have defined first and last terms,otherwise,infinite sequences and series continue indefinitely.Infinite series need tools from mathematical analysis,which are also widely used in other quantitative disciplines such as physics,computer science,and finance.Now we have an infinite sequence a_1,a_2,  相似文献   

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We propose a class assignment where students are asked to construct and implement an efficient algorithm to calculate the last digits of a positive integral power of a positive integer. The mathematical prerequisites for this assignment are very limited: knowledge of remainder calculus and the binary representation of a positive integer. The periodicity of the last digits is studied by means of the Euler totient function and the Carmichael function.  相似文献   

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In virtue of what does a linguistic act count as an insult? I discuss five main approaches to this question, according to which an insult is determined by (i) the semantic properties of the expression used; (ii) the insulter, her intention, or attitudes; (iii) the addressee and her personal standard; (iv) the features of the speech act performed; and (v) the standard of the relevant social group. I endorse the last, objectivist account, according to which an act x counts as an insult if and only if x is assessed as demeaning when addressed at A by the standard of the relevant social group at t.  相似文献   

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Cyber risks are high on the business agenda of every company, but they are difficult to assess due to the absence of reliable data and thorough analyses. This paper is the first to consider a broad range of cyber risk events and actual cost data. For this purpose, we identify cyber losses from an operational risk database and analyze these with methods from statistics and actuarial science. We use the peaks-over-threshold method from extreme value theory to identify “cyber risks of daily life” and “extreme cyber risks”. Human behavior is the main source of cyber risk and cyber risks are very different compared with other risk categories. Our models can be used to yield consistent risk estimates, depending on country, industry, size, and other variables. The findings of the paper are also useful for practitioners, policymakers and regulators in improving the understanding of this new type of risk.  相似文献   

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This article outlines a conception of perceptual-recognitional abilities. These include abilities to recognize certain things from their appearance to some sensory modality, as being of some kind, or as possessing some property. An assumption of the article is that these abilities are crucial for an adequate understanding of perceptual knowledge. The specific aim here is to contrast those abilities with abilities or competences as conceived in the virtue-theoretic literature, with particular reference to views of Ernest Sosa and John Greco. In the course of the discussion, it is emphasized that the notion of exercising a perceptual-recognitional ability is a success notion: exercising such an ability is nothing less than acquiring knowledge. Even so, the view can make sense of our fallibility. It can also be defended in the face of an objection stemming from consideration of what are here called success-rate abilities.  相似文献   

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