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

The shape of a graph, The Shape of a Graph, Part II : In previous we saw h...

The Shape of a Graph, Part II : In previous we saw how we could use the first derivative of a function to obtain some information regarding the graph of a function.  In this secti

World Problems on simultaneous equations, A particular algebra text has a t...

A particular algebra text has a total of 1382 pages which is broken up into two parts. the second part of book has 64 more pages than first part. How many pages are in each part of

Lognormal distribution, The Lognormal Distribution If ln(X) is a normal...

The Lognormal Distribution If ln(X) is a normally distributed random variable, then X is said to be a lognormal variable. If P1, P2, P3, ... are the prices of a scrip in per

Solution by factorization, Solution by Factorization, please solve quadrati...

Solution by Factorization, please solve quadratic equations by Factorization.

Domain and range of a relation, Consider R be a relation from A to B, that ...

Consider R be a relation from A to B, that is, take R A Χ B. Then Domain R = {a: a € A, (a, b) € R for any b € B} i.e. domain of R is the set of all the first components of

Linear approximations, Linear Approximations In this section we will l...

Linear Approximations In this section we will look at an application not of derivatives but of the tangent line to a function. Certainly, to get the tangent line we do have to

Solving decimal equations, The distance around a square photograph is 12.8 ...

The distance around a square photograph is 12.8 centimeters. What is the langth of each side of the fotograph?

Derivatives of hyperbolic functions , Derivatives of Hyperbolic Functions ...

Derivatives of Hyperbolic Functions : The last set of functions which we're going to be looking at is the hyperbolic functions.  In several physical situations combinations of e

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