Solve the recurrence relation, Mathematics

Assignment Help:

Solve the recurrence relation

T (K) = 2T (K-1), T (0) = 1

Ans: The following equation can be written in the subsequent form: 

tn - 2tn-1 =  0 

Here now successively replacing n by (n - 1) and then by (n - 2) and so on we obtain a set of equations.

The method is continued till terminating condition. Add these equations in such type of a way that all intermediate terms get cancelled. The equation can be rearranged as 

1709_Solve the recurrence relation.png

Multiplying all the equations correspondingly by 20, 21, ..., 2n - 1 and then adding them together, we get

tn - 2nt0 = 0 

or,  tn = 2n


Related Discussions:- Solve the recurrence relation

John 47 out of 86 free-throws who best free-throw shooter, Michael made 19 ...

Michael made 19 out of 30 free-throws this basketball season. Larry's freethrow average was 0.745 and Charles' was 0.81. John made 47 out of 86 free-throws. Who is the best free-th

Maths For Fun, Ask Suppose I offer you a loan to start a safety matchstick ...

Ask Suppose I offer you a loan to start a safety matchstick production unit on the following terms: I shall first advance you Rs.50,000/- to set up your unit, and wait for 3 month

Constructing a dfa/nfa or a regex), Let ∑ = (0, 1). Define the following la...

Let ∑ = (0, 1). Define the following language: L = {x | x contains an equal number of occurrences of 01 and 10} Either prove L is regular (by constructing a DFA/NFA or a rege

What is polygon, What is polygon? A polygon is a shape with three or mo...

What is polygon? A polygon is a shape with three or more sides, in which each side touches another only at its endpoints. Some polygons that you are probably already familiar w

Sketch several trajectories for the system, Sketch several trajectories for...

Sketch several trajectories for the system, x 1 ' = x 1 + 2x 2                                                                                x 2 ' = 3x 1 + 2x 2

Decision tree analysis, DECISION TREE ANALYSIS The Finance Manager of ‘...

DECISION TREE ANALYSIS The Finance Manager of ‘Softy’ baby soap manufacturing company being successful in the first two years of the company’s operations is considering to set

Application of statistics-human resource management, Human resource managem...

Human resource management Statistics may be utilized in efficient employ of human resources for example we may provide questionnaires to workers to find out where the manageme

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd