Solved

Recurrence relation with Square roots in each term..

Posted on 2004-03-22
9
593 Views
Last Modified: 2011-08-18
Hi experts,
    How to solve a recurrence relation that have Square roots in each term...

    I can solve the normal recurrence relation problem (that hav no square roots)

    Give me some idea...

    Q will be like this

   ROOT(Rn) = ROOT(Rn-1)+ 2.ROOT(Rn-2)  with initial condition R0=R1=1

Rosh :)
0
Comment
Question by:Roshan Davis
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 5
  • 4
9 Comments
 
LVL 84

Expert Comment

by:ozo
ID: 10655843
Rn = Sn²
where
Sn = (Sn-1) + 2×(Sn-2)
0
 
LVL 23

Author Comment

by:Roshan Davis
ID: 10655884
Thankx for ur comment :)

Calculated associated equation
square(X) = X + 2
and itz roots are (x-2)(x+1)

C1 = u(-1)+v(2)
C2 = u.square(-1)+ v. square(2)

And reached the result

Cn = (-1/3)(-1)^n + (1/3)(2)^n

this is the Recurrence relation for "Sn = (Sn-1) + 2×(Sn-2)"

Is this correct?

Rosh :)
0
 
LVL 84

Expert Comment

by:ozo
ID: 10655919
or in closed form
Rn = (((-1)^n+2^(n+1))/3)^2
0
Independent Software Vendors: We Want Your Opinion

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

 
LVL 84

Expert Comment

by:ozo
ID: 10655927
Sorry, didn't see you had solved it
0
 
LVL 23

Author Comment

by:Roshan Davis
ID: 10655941
But answers were different...?
Can u show me some steps...
0
 
LVL 23

Author Comment

by:Roshan Davis
ID: 10655984
Hi, you can see the question here http://www.coolgoose.com/sites/puttalu/
0
 
LVL 84

Expert Comment

by:ozo
ID: 10656001
They were different because you used C1=C2=1, while I used R0=R1=1
0
 
LVL 23

Author Comment

by:Roshan Davis
ID: 10656009
So, for this Q http://www.coolgoose.com/sites/puttalu/ which is correct ?
Rosh :)
0
 
LVL 84

Accepted Solution

by:
ozo earned 125 total points
ID: 10656073
for r0=r1=1
Rn = (((-1)^n+2*2^n)/3)^2
is correct
((-1)^0 + 2*2^0)/3 = 1
((-1)^1 + 2*2^1)/3 = 1
0

Featured Post

Free Tool: Site Down Detector

Helpful to verify reports of your own downtime, or to double check a downed website you are trying to access.

One of a set of tools we are providing to everyone as a way of saying thank you for being a part of the community.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Article by: Nicole
This is a research brief on the potential colonization of humans on Mars.
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…

710 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question