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Holt McDougal Algebra 2
Holt McDougal Algebra 2

... In the Fibonacci sequence, the first two terms are 1 and each term after that is the sum of the two terms before it. This can be expressed by using the rule a1 = 1, a2 = 1, and an = an – 2 + an – 1, where n ≥ 3. This is a recursive formula. A recursive formula is a rule in which one or more previous ...
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... Infinite # of elements: {an | n is even}, {an | n is prime}, {an | n is a perfect square} ...
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On the rational approximation to the binary Thue–Morse–Mahler
On the rational approximation to the binary Thue–Morse–Mahler

Recurrence relations and generation functions
Recurrence relations and generation functions

... Let hn denote the number of non-nagative integral solutions of the equation 3e1 + 4e2 + 2e3 + 5e4 = n. Find the generating function g(x) for h0, h1, h2, …, hn,……. Hints: change the variable by let f1 = 3e1, f2 = 4e2, f3 = 2e3 and f4 =5e4. Then hn also equals the number of non-negative integral solut ...
Solutions - New Zealand Maths Olympiad Committee online
Solutions - New Zealand Maths Olympiad Committee online

... s , of C and t = s/ 2, so s = s/3 i.e. the ratio of the side lengths is 3. 5. Consider functions f from the whole numbers (non-negative integers) to the whole numbers that have the following properties: • For all x and y, f (xy) = f (x)f (y), • f (30) = 1, and • for any n whose last digit is 7, f (n ...
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... Integers." College Math. J. 26 (1995):118-23. 12. E. B. Shanks. "Iterated Sums of Powers of the Binomial Coefficients." Amer. Math. ...
Analytic Functions
Analytic Functions

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AP Calculus AB

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4.5 Find a Pattern in a Sequence

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... Introducing sequences In maths, we call a list of numbers in order a sequence. ...
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... Find the terms of a sequence, including a recursively defined sequence. Find the partial sums of a sequence. Find the sum of a sequence defined using sigma notation. Write a sum using sigma notation. ...
WHAT IS THE NEXT NUMBER IN THIS SEQUENCE?
WHAT IS THE NEXT NUMBER IN THIS SEQUENCE?

... pattern questions have been useful as training in recognising patterns and appreciation of mathematics. What is needed in such texts is an insertion somewhere that such questions as they stand are ‘nonsense’ if there is no assumption about the sequence. One should also add that a sequence is only de ...
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Notes on Infinite Sets

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- Deer Creek High School

Trig Course Outline - Northwest Arkansas Community College
Trig Course Outline - Northwest Arkansas Community College

吴 鹏老师
吴 鹏老师

... if the difference of any two consecutive terms is constant. This difference is called the common ...
Normal numbers without measure theory - Research Online
Normal numbers without measure theory - Research Online

Delta Function and Optical Catastrophe Models  Abstract
Delta Function and Optical Catastrophe Models Abstract

... presented in Engineering, and in Physics, and its singularity does not disappear when it is presented as a Generalized Functional in Mathematics. We have shown that the Delta Function is a Hyper-real Function defined on the hyper-real line, an infinite dimensional line that has room for infinitesima ...
1.4 Limits and Continuity
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Microsoft Word Viewer
Microsoft Word Viewer

Density functions Math 217 Probability and Statistics
Density functions Math 217 Probability and Statistics

... where, it will equal f . Typically F will be differreal random variable X has a cumulative distribuentiable everywhere or perhaps everywhere except tion function FX : R → [0, 1] defined as one or two points. About the graphs of f and F . The cuFX (b) = P (X ≤ b). mulative distribution function F is ...
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Series (mathematics)

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