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:

t_n - 2t_n-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, ..., 2^{n - 1} and then adding them together, we get

t_n - 2ⁿt₀ = 0

or, t_n = 2_n

Related Discussions:- Solve the recurrence relation

Help please, 1

Determine the laplace transform of the probability , 1. Let , where ar...

1. Let , where are independent identically distributed random variables according to an exponential distribution with parameter μ. N is a Binomially distribut

Cross product - vector, Cross Product In this last section we will loo...

Cross Product In this last section we will look at the cross product of two vectors. We must note that the cross product needs both of the vectors to be three dimensional (3D

Prove that a/b+c-a, a, b,c are in h.p prove that a/b+c-a, b/a+c-b, c/a+b-c ...

a, b,c are in h.p prove that a/b+c-a, b/a+c-b, c/a+b-c are in h.p To prove: (b+c-a)/a; (a+c-b)/b; (a+b-c)/c are in A.P or (b+c)/a; (a+c)/b; (a+b)/c are in A.P or 1/a; 1

Algebra2;, log6 X + log6 (x-5) = 1

log6 X + log6 (x-5) = 1

Pre Calculus, 5 2 --- - --- x-1 x+1

5 2 --- - --- x-1 x+1

Quotient rule, Quotient Rule : If the two functions f(x) & g(x) are differ...

Quotient Rule : If the two functions f(x) & g(x) are differentiable (that means the derivative exist) then the quotient is differentiable and,

Differential calculus, lim n tends to infintiy ( {x} + {2x} + {3x}..... +{n...

lim n tends to infintiy ( {x} + {2x} + {3x}..... +{nx}/ n2(to the square) )where {X} denotes the fractional part of x? Ans) all no.s are positive or 0. so limit is either positive

How many students are study physics alone, A class has 175 learners. The gi...

A class has 175 learners. The given table describes the number of learners studying one or more of the subsequent subjects in this case Subjects

Explain identifying conic sections, Explain Identifying Conic Sections ...

Explain Identifying Conic Sections The graph of a quadratic equation in the variables x and y, like this one, x 2 + 3y 2 + 6y = -4, is a conic sections. There are three kind

Write Your Message!

Name

Email id

Message

Verfication Code

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!

Submit Assignment

User Account

All Pages