Hello everyone (Hi)

I really need help on this work:

Solve 4an+2 - 4an+1 + an = (1/3)^n

Thanks in anticipation :)

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- Oct 24th 2009, 06:39 AMRmathkNon-homogeneous recurrence relations
Hello everyone (Hi)

I really need help on this work:

Solve 4an+2 - 4an+1 + an = (1/3)^n

Thanks in anticipation :) - Oct 24th 2009, 09:19 AMHallsofIvy
If $\displaystyle a_n$ is the general solution to the associated homogeneous equation, $\displaystyle 4a_{n+2}- 4a_{n+1}+ a_n= 0$, and $\displaystyle b_n$ is any solution to the entire equation, $\displaystyle 4a_{n+2}- 4a_{n+1}+ a_n= (\frac{1}{3})^n$, then $\displaystyle a_n+ b_n$ is the general solution to the entire equation.

Do you know how to find the general solution to the associated homogeneous equation?

To find a solution to the entire equation, try a particular solution $\displaystyle b_n= A\left(\frac{1}{3}\right)^n$. - Oct 24th 2009, 07:55 PMRmathk
- Oct 24th 2009, 11:52 PMCaptainBlack