- Find the closed form for the following series:a) 1+ 2 + 3 + 5 + ... + nb) 1+ x2+ x3 ++ x* where x is constant and x > 1...c) 1+ x2 + x3 ++ x" where x is constant and x < 1...d) 1+ (1/2) + (1/3) + ... + (1/n)

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Answered: - Find the closed form for the…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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2.) Q = {A, B} S = {a,b,c,d,e,f...z} qi = {A} F = {B} P = state A B a,b,c,d,e,f...y A B 28 B B
Question Number Four: Answer each one of the following questions in the space assigned: 1- Simplify each of the following expressions using boolean algebra identities: [4 Marks] a- AB + A( CD + CD') b- ( BC' + A'D) ( AB' + CD') 2- Optimize (simplify) the following boolean function F together with the don't care conditions d in Product-of-sums using k-map: F(A,B.C.D) = IIM (1,3,4,6,9,11)+Ed (0,2,5,8,10,12,14)
A) Shanon Code B) Shanon-Fano Code for the following Set of massages: [P(X)] =x*.s*04 02 021 X 2 хз х 4 X5 0.05 0.15 0.4 0.2 0.2 Find the code efficiency ?
******** 6. The Product of sum (POS) form for the function F(X, Y, Z) = (1,5, 6, 7) is.
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Let's take a look at the steps needed to be performed for each operation.The prefix (++x) increment must perform the following steps:
Eliminate useless variables and symbols. Afterwards, convert to Chomsky Normal Form. (Start variable S) S -> ABBC | BA A-> abB | aa B -> bB | Aa C -> Cb | aC
F= (~A xor ~B) or ~CF= ~A or ~B or ~CF= ((~A or B) and (~A or ~B)) or (C+~A) Use the functions above to create digital circuits.2- Use Boolean Algebra to simplify the following functions.F= (~A+B) (A+B)(C+A)F= ABC+ A(~B+~C)+C(A+B)F=(A+B)(A+C)(B+C)
(a) If r and s are regular expressions, explain why (r+s)* + r* + s* . (b) Also carefully explain why (r*s*)* = (r + s)* .
(1) (a) Let r, 1, and r, be regular expression. Find all the regular ones from the following expression s: 2, r'-0. ((r')). r), n -n +½. (b) Given a regular expression 7; = a(ab)* +b°a*, r, = (b + a)* +a*, find L(;) and L(r,), the languages associated with i and r3, respective ly. (c) Find a regular expression r such that L(r) is the same as L = {b"ab",(ba)* : n, m2 0,h2 1}. %3D
Write and test a recursive C-function that calculates the series: 1+2+3+4+5+.........+N.
Write the distributive law:

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- Find the closed form for the following series: a) 1+2 +3 + 5 + ... + n b) 1+ x2 + x3 + + x" where x is constant and x > 1 ... c) 1+ x2 + x3+ + x" where x is constant and x < 1 ... d) 1 + (1/2) + (1/3) + ... + (1/n)