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

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SUMMARY

The discussion centers on the convergence of the recurrence relation defined by x[n] = 0.5(x[n-1] + x[n-2]) with initial values x[0] = 3 and x[1] = 5. Participants clarify that the main inquiry is whether the sequence converges to the proposed limit of 13/3 as n approaches infinity. The conversation emphasizes the importance of clearly stating the problem and adhering to appropriate forum sections for academic inquiries.

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Buddy711
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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.
 
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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.
 

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