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Give a recursive definition of the sequence {a,,}, n = 1,2, 3 .if| b) а, — п(п + 1) n2 a) а, 3 4n — 2 c) a, = 1+ (-1)" d) an

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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Concept explainers

Computational Systems

The computation systems can be defined as the systems that are capable of solving a problem that includes calculations either mathematical or logical, and are able to produce the result as an output. For example, a simple calculator that is given a set of numbers and operators as input and produces the result as an output can be defined as a computational system. The above example is a simple illustration only, the computational systems range from simple devices to complex devices such as the systems that control the SpaceX companies, Starlink satellites which are being quite recently seen in the skies at many places globally.

Question

Give a recursive definition of the sequence {a,,}, n = 1,2, 3 .if|
b) а, — п(п + 1)
n2
a) а, 3 4n — 2
c) a, = 1+ (-1)"
d) an

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Let ∑={a,b} and T be the set of words in ∑* that have an equal number of a’s and b’s. (a) Give a recursive definition for the set T. (b) Show that abbaba is in T by building up from the base case through recursion. (c) Is your recursive definition uniquely determined?
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write a c++ recursive function to solve the following: str contains a single pair of parenthesis, return a new string // made of only the parenthesis and whatever those parensthesis contain. You can use substr in this problem. // // Pseudocode Example:// findParen("abc(ghj)789") => "(ghj)" // findParen("(x)7") => "(x)" // findParen("4agh(y)") => "(y)" // string findParen(string str) { }
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Let ∑={a,b} and T be the set of words in ∑* that have no consecutive a’s (i.e. there cannot be 2 or more a’s in a row). (a) Give a recursive definition for the set T. (b) Use your recursive definition to show that the string “abbaba” is in T. (c) Is your recursive definition uniquely determined? Explain why or why not.
Question 4
solve by hand do not use code