Roshan Davis
asked on
Recurrence relation with Square roots in each term..
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 :)
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 :)
ASKER
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 :)
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 :)
or in closed form
Rn = (((-1)^n+2^(n+1))/3)^2
Rn = (((-1)^n+2^(n+1))/3)^2
Sorry, didn't see you had solved it
ASKER
But answers were different...?
Can u show me some steps...
Can u show me some steps...
ASKER
Hi, you can see the question here http://www.coolgoose.com/sites/puttalu/
They were different because you used C1=C2=1, while I used R0=R1=1
ASKER
So, for this Q http://www.coolgoose.com/sites/puttalu/ which is correct ?
Rosh :)
Rosh :)
ASKER CERTIFIED SOLUTION
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where
Sn = (Sn-1) + 2×(Sn-2)