EBK JAVA HOW TO PROGRAM, LATE OBJECTS
EBK JAVA HOW TO PROGRAM, LATE OBJECTS
11th Edition
ISBN: 9780134763507
Author: Deitel
Publisher: VST
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Chapter 3, Problem 1.14SRE
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A “floating-point number” is a number which contains a decimal part in it, such as 7.33, 0.0975, or 1000.12345.

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2 3 4 5 The following are some examples of Krishnamurthy numbers: 6 7 8 9 0 1 2 3 A Krishnamurthy number is a number whose sum total of the factorials of each digit is equal to the number itself. 4 5 "145" is a Krishnamurthy Number because, 1! + 4! + 5! = 1 + 24 + 120 = 145 "40585" is also a Krishnamurthy Number. 4 + 0 + 5! +8! + 5! = 40585 "357" or "25965" is NOT a Krishnamurthy Number 3! + 5 + 7! = 6 + 120 + 5040 != 357 6 The following function will check if a number is a Krishnamurthy Number or not and return a 7 boolean value. 8 ***
Exercise III: Catalan numbers For n e N, denote by c, to be the number of ways to form a "mountain range" with n upstrokes (U) and n downstrokes (D) that all stay above a horizontal line. For instance: for n = 1, only UD is allowed, so c = 1; • for n = 2, only UUDD and UDUD are allowed, so c2 = 2. 1. Check that c3 = 5 by writing down or drawing all possible options. 2. Consider the power series +00 g(x) = 2 n=0 (by definition co = 1) called the generating function of the sequence (en). Justify that cn < 4" for each n, and deduce that the radius of convergence of g is at least 1/4. 3. It can be show that for r E (-1/4, 1/4), g(x) = 1+ xg(r)? and therefore 1- VI 4.x g(x) = 2.x Use this formula and the known power series of V1+ x to write the first terms of the power series expansion of g, in the form g(x) = co + c1x + c2x2 + C3x + c4x* + ·.. Show how you obtain a few terms, but you do not need to show all computations and you can use a calculator for fractions. Check that you recover co,…
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EBK JAVA HOW TO PROGRAM, LATE OBJECTS

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