Solved

Recurrence relation with Square roots in each term..

Posted on 2004-03-22
9
592 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
Industry Leaders: 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: IP Lookup

Get more info about an IP address or domain name, such as organization, abuse contacts and geolocation.

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

Title # Comments Views Activity
Relative Frequency 5 61
Graph 2 108
How to get the score in percent of an activity? 7 67
Calculation of speed from point A to point B. 4 30
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
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…
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…

740 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