Finding the Convergence of an Equation - x[n] = 0.5(x[n-1]+x[n-2])

  • Thread starter Buddy711
  • Start date
In summary, the conversation discusses a recurrence relation with an initial value and a proposed limit. The question posed is unclear and it is suggested to post in the Homework Help section.
  • #1
Buddy711
8
0
hi all.
I am very confusing there exists such a convergent number of this equation.

x[n] = 0.5(x[n-1]+x[n-2])

with the initial value x[0]=3, x[1]=5
if n goes infinity, x[n] may go to 13/3.

How can I approach this problem?

thanks.
 
Mathematics news on Phys.org
  • #2
You have described a recurrence relation and proposed a limit for it, but we don't know the question you are asking?

Are you asking whether or not that sequence converges at all, or to that particular numer 13/3 ? What is the exact wording of the problem you were given?

Furthermore: This isn't even the Homework help section! Please in the future create these threads in that section.
 

FAQ: Finding the Convergence of an Equation - x[n] = 0.5(x[n-1]+x[n-2])

What does it mean to find the convergence of an equation?

Finding the convergence of an equation means determining whether the values of the equation will approach a certain limit or value as the number of iterations or steps increases. In other words, it involves finding out if the equation will eventually stabilize or continue to fluctuate.

How does the equation x[n] = 0.5(x[n-1]+x[n-2]) relate to convergence?

This equation is a recursive formula, which means it uses previous values to calculate the next value. By repeatedly applying this formula, we can see if the values eventually converge or not.

What factors affect the convergence of this equation?

The convergence of this equation can be affected by the initial values of x[n-1] and x[n-2], as well as the value of the constant 0.5. It can also be influenced by the behavior of the equation as n approaches infinity.

How can we determine the convergence of this equation?

To determine the convergence of this equation, we can calculate and compare the values of x[n] for different values of n. If the values start to approach a specific limit or value, then we can say that the equation is converging. However, if the values continue to fluctuate or diverge, then the equation is not converging.

Why is it important to find the convergence of an equation?

Finding the convergence of an equation can help us understand the behavior and stability of the equation. It can also be useful in various fields such as mathematics, physics, and engineering, where recursive formulas and iterative processes are commonly used. Additionally, knowing if an equation is converging or not can help us make predictions and improve our understanding of complex systems.

Similar threads

B Popularizing a property for n-bonacci numbers without publishing it?
Replies
12
Views
1K
MHB Solve Integer & Inequality: $x=(x-1)^3$ for $N$
Replies
1
Views
947
MHB Solve Floor Equation 7: x^2=2x-1
Replies
2
Views
1K
A Rich "isotropic tensor" concept
Replies
1
Views
1K
MHB For which values of a can we solve it iteratively?
Replies
10
Views
1K
I Is there any solution to the equation x^(0.5)+1=0?
Replies
15
Views
2K
MHB Limit of integral challenge of (e^(-x)cosx)/(1/n+nx^2)
Replies
2
Views
1K
I Method for finding a complex series?
Replies
10
Views
801
I What is meant by "convergent just preceding ##\frac{a}{b}##" ?
Replies
2
Views
1K
MHB Solve √(x^2+3x+7)-√(x^2-3x+9)+2=0
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top