Rahul Chacko IB Mathematics HL Revision – Step One Chapter 1.1 – Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series. Sigma notation. Arithmetic Sequences Definition: An arithmetic sequence is a sequence in which each term differs from the previous one by the same fixed number: {un} is arithmetic if and only if u n 1 u n d . Information Booklet u n u1 n 1d Proof/Derivation: u n 1
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Questionbank Topic 1. Sequences and Series‚ Exponentials and The Binomial Theorem 1. Find the sum of the arithmetic series 17 + 27 + 37 +...+ 417. 2. Find the coefficient of x5 in the expansion of (3x – 2)8. 3. An arithmetic series has five terms. The first term is 2 and the last term is 32. Find the sum of the series. 4. Find the coefficient of a3b4 in the expansion of (5a + b)7. 5. Solve the equation 43x–1 = 1.5625 × 10–2. 6. In an arithmetic sequence‚ the first term is 5 and the
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found that the Fibonacci numbers appear anywhere from leafs on plants‚ patterns of flowers‚ in fruits‚ some animals‚ even in the human body. Could this be nature’s numbering system? For those who are unfamiliar with the Fibonacci numbers they are a series of numbers discovered by Leonardo Fibonacci in the 12th century in an experiment with rabbits. The order goes as follows: 1‚ 1‚ 2‚ 3‚ 5‚ 8‚ 13‚ 21‚ 34‚ 55‚ 89‚ 144‚ 233‚ 377‚ 610 and so on. Starting with 1‚ each new number is simply the sum of the
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Trương Thành Nam Hướng dẫn: Ths. Đặng Thị Bích Thảo MSSV: 1400056 Essay project 2 Pierre Robin Sequence Introduction : Pierre Robin sequence (PRS) is a rare congenital defect‚ which was first described by Lannelongue Menard in 1891 as Pierre Robin syndrome. The word “syndrome” then was replaced by “sequence” because the pathogenesis of the condition occurs through a chain of events. The sequence include small jaw (micrognathia)‚ displacement of the tongue (glossoptosis) which consequence to airway
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ROUND -1 SEATING ARRANGMENT 1. | A‚ P‚ R‚ X‚ S and Z are sitting in a row. S and Z are in the centre. A and P are at the ends. R is sitting to the left of A. Who is to the right of P ? | | A. | A | B. | X | C. | S | D. | Z | 1. Answer: Option BExplanation:The seating arrangement is as follows:Therefore‚ right of P is X. | 2. | There are 8 houses in a line and in each house only one boy lives with the conditions as given below: 1. Jack is not the neighbour Siman. 2. Harry is just next
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Sequence stratigraphy Sequence stratigraphy is a method of stratigraphic interpretation that combines the chronological order of the accumulation of sediments‚ their stratal architecture and the geometric relationships of their facies to determine depositional setting and predict stratal continuity. The workflow of sequence stratigraphic analysis first identifies the genetic units and bounding surfaces that compose the stratigraphic section in outcrop‚ core‚ well-log and seismic data. The framework
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Chandreyee Chatterjee Sequence Analysis October 30‚ 2014 Sequence Analysis Step 2: 1. The establishing shot of Hannibal behind the curtain reveals that he will be the main focus of the sequence. The scene was shot from a 3rd person point of view perspective‚ which makes it seem like there is a 3rd person it inside the jail cell with him. This kind of perspective allows the audience to anticipate what is to come further along scene. 2. The score creates an almost melancholy mood‚ letting the audience
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Sequence Essay In a sequence essay‚ you are writing to describe a series of events or a process in some sort of order. Usually‚ this order is based on time. You organize the essay by writing about each step of the process in the order it occurred. Example question: | Write an essay outlining the stages of the salmon life cycle. | Introduction: | Describe what a salmon is like. | Supporting paragraphs: | 1. Describe young salmon. | | 2. Describe adult salmon. | | 3. Describe what salmon
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The Fibonacci sequence The Fibonacci sequence is a series of numbers developed by Leonardo Fibonacci as a means of solving a practical problem. The original problem that Fibonacci investigated‚ in the year 1202‚ was about how fast rabbits could breed in ideal circumstances. Suppose a newly born pair of rabbits‚ one male‚ one female‚ are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that
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TIME SERIES ANALYSIS Chapter Three Univariate Time Series Models Chapter Three Univariate time series models c WISE 1 3.1 Preliminaries We denote the univariate time series of interest as yt. • yt is observed for t = 1‚ 2‚ . . . ‚ T ; • y0‚ y−1‚ . . . ‚ y1−p are available; • Ωt−1 the history or information set at time t − 1. Call such a sequence of random variables a time series. Chapter Three Univariate time series models c WISE 2 Martingales Let {yt} denote
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