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- Nov 14th 2011, 11:30 AMgreg1987solve equation
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- Nov 14th 2011, 11:38 AMQuackyRe: solve equation
What do you mean "solve equation"? There isn't anything to solve. You have a recurrence relation. What is the exact wording of the question?

- Nov 14th 2011, 11:44 AMgreg1987Re: solve equation
IN this case we don't want recurrence relationship, we need determine using only.

- Nov 14th 2011, 02:15 PMSorobanRe: solve equation
Hello, greg1987!

Have you been taughtabout recurrence relations?*anything*

It's impossible to help you if I don't know what you have learned so far

. . and where you are having difficulty.

Quote:

. .

By the way, the answer is:.

- Nov 15th 2011, 12:31 AMsbhatnagarRe: solve equation
- Nov 15th 2011, 01:19 AMmr fantasticRe: solve equation
- Nov 17th 2011, 04:48 AMHallsofIvyRe: solve equation
For "linear recurrences with constant coefficients", things such as where b and c are numbers, there is a very general method: first drop the number that is not multiplying and "a": and "try" . Then so the equation becomes and, dividing both sides by , r= b. That is satisfies . In fact it is easy to see that any constant times that, , is a solution. To find a solution to the entire equation, "try" a constant: if the equation becomes so and (if b is not 1), . The solution to the entire equation is the sum of those: for any constant p. (If b= 1, the equation is and we have an arithmetic sequence.)

This same idea can be used for higher order recurrences: If we have , setting gives [tex]r^{n+2}= 3r^{n+1}- 2r^n[tex] and dividing through by and moving everything to the left, . That is, both and satisfy the recurrence and the general solution is for any constants, A and B.