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

Math, how to compare fractions

how to compare fractions

Help with word problem, You would like to have $4000 in four years for a sp...

You would like to have $4000 in four years for a special vacation following graduation by making deposits at the end of every 6 months in an annuity that pays 7% compounded semiann

Reduced Row-Echelon Form, The augmented matrix from a system of linear equa...

The augmented matrix from a system of linear equations has the following  reduced row-echelon form (a)  How many equations are there in the system?  (b)  How many variab

Left-handed limit, Left-handed limit We say provided we can mak...

Left-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x Note that the change in notation is extremely m

Theorem on intervals of validity, Theorem Consider the subsequent IVP....

Theorem Consider the subsequent IVP. y′ =  p (t ) y = g (t )  y (t 0 )= y 0 If p(t) and g(t) are continuous functions upon an open interval a o , after that there i

Interpretations of definite integral, Interpretations of Definite Integral ...

Interpretations of Definite Integral There are some quick interpretations of the definite integral which we can give here. Firstly, one possible interpretation of the defini

Prove that xa+ar=xb+br of circle, In figure, XP and XQ are tangents from X ...

In figure, XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA+AR=XB+BR Ans:    Since the length of tangents from externa

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