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

Identify the flaw in the argument, Identify the flaw in the following argum...

Identify the flaw in the following argument which supposedly determines that n 2 is even when n is an even integer. As well name the reasoning:             Assume that n 2 is

Triangles are resolute, a) How many equivalence relations on {a, b, c, d, e...

a) How many equivalence relations on {a, b, c, d, e, f} have b)  How many arrangements are there of c)  How many triangles are resolute by the vertices of a regular polygon w

gauss elimination method , Question: Use  Gauss elimination method to ...

Question: Use  Gauss elimination method to solve the following system of equations.  -y +3z=4  2x-y-2z= 2  2x-2y+z =6  4x-y-7z= 0

Alzebra, how can i memorize the formulas

how can i memorize the formulas

Boundary value problem, solve the in-homogenous problem where A and b are c...

solve the in-homogenous problem where A and b are constants on 0 ut=uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0 u(1,t)=-A/b^2 exp(-b)

Describe vibration absorber and white noise, Describe what is meant by eac...

Describe what is meant by each of the following NVH terms and explain their importance in vehicle refinement: (a)  Vibration absorber (b)  Fast Fourier Transform (c)  Whit

Substitution rule, Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (...

Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (u ) du,     where, u = g ( x ) we can't do the following integrals through general rule. This looks considerably

Basic set union operation, Q. Basic Set Union Operation? Ans. Supp...

Q. Basic Set Union Operation? Ans. Suppose instead that your school needs to know which students are taking either art or business or both. Then the students who are ta

Matrices, suppose you a business owner and selling cloth. the following rep...

suppose you a business owner and selling cloth. the following represents the number of items sold and the cost for each item. use matrix operation to determine the total revenue ov

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