Find the solution to the recurrence relation an=2nan-1 with the initial condition ao = 3 using an iterative approach by the given following procedure. an=2nan-1 = 2n(2(n-1)an-2) = 2²(n(n-1))an-2 = 22(n(n-1))(2(n − 2)an-3) = 2³(n(n-1)(n − 2))an-3 = ........continuing in the same manner = 2^n(n-1)(n-2)(n-3)....(n-(n-1))an-n = 2^n(n – 1)(n – 2)(n – 3)...1.ao 3.2" n! 2n n! 3.2" (n+1)! O 3.2" (n-1)!

Find the solution to the recurrence relation an=2nan-1 with the initial condition ao = 3 using an iterative approach by the given following procedure. an=2nan-1 = 2n(2(n-1)an-2) = 2²(n(n-1))an-2 = 22(n(n-1))(2(n − 2)an-3) = 2³(n(n-1)(n − 2))an-3 = ........continuing in the same manner = 2^n(n-1)(n-2)(n-3)....(n-(n-1))an-n = 2^n(n – 1)(n – 2)(n – 3)...1.ao 3.2" n! 2n n! 3.2" (n+1)! O 3.2" (n-1)!

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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Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.

Question

Find the solution to the recurrence relation an = 2nan-1 with the initial condition ao = 3 using an iterative approach by the given following procedure.
an=2nan-1
= 2n(2(n-1)an-2)
2²(n(n-1))an-2
= 2²(n(n-1))(2(n-2) an-3)
= 2³ (n(n-1)(n-2))an-3
= ........continuing in the same manner
=
2^n(n-1)(n-2)(n-3)....(n-(n-1))an-n
= 2^n(n – 1)(n – 2)(n – 3)....1.ao
=
3.2" n!
2n!
3.2" (n+1)!
O 3.2" (n-1)!

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