Solved

# Recurrence relation with Square roots in each term..

Posted on 2004-03-22
593 Views
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
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
• 5
• 4

LVL 84

Expert Comment

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

LVL 23

Author Comment

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

ID: 10655919
or in closed form
Rn = (((-1)^n+2^(n+1))/3)^2
0

LVL 84

Expert Comment

ID: 10655927
Sorry, didn't see you had solved it
0

LVL 23

Author Comment

ID: 10655941
Can u show me some steps...
0

LVL 23

Author Comment

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

LVL 84

Expert Comment

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

LVL 23

Author Comment

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

LVL 84

Accepted Solution

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

Question has a verified solution.

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

### Suggested Solutions

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…
###### Suggested Courses
Course of the Month2 days, 5 hours left to enroll
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}