MHB Solve Constant Alpha's in Images: Help to Understand and Get Unstuck

AI Thread Summary
The discussion revolves around solving a problem related to constant alpha's in images, specifically focusing on finding the closed-form solution for a characteristic root of multiplicity 3, which is identified as r = -1. The correct closed-form solution is given as a_n = (-1)^n(c_1 + c_2n + c_3n^2), emphasizing the need to include "n" due to the repeated root. Participants also address the challenge of writing mathematical notation directly in the forum, with a suggestion to use LaTeX for proper formatting. A tutorial link for LaTeX usage is provided to assist users in improving their mathematical expression presentation. Overall, the thread highlights both the mathematical solution and the technical aspects of sharing math work online.
yakin
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The book answer is 1, 3 and -2. I can't figure how they got it? Please help to understand and help me to get through where i got stuck.

Please look at images from bottom page to top page(where you see crossing on a page)
 

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You have correctly found that the characteristic root is $r=-1$ of multiplicity 3, however, you have not properly dealt with the fact that the root is repeated. Since this root is of multiplicity 3, the closed-form will be:

$$a_n=c_1(-1)^n+c_2n(-1)^n+c_3n^2(-1)^n=(-1)^n\left(c_1+c_2n+c_3n^2 \right)$$
 
Thank you for your feedback. I noticed that. I forgot to stick "n" in the general form of the solution with the repeated roots. Thanks though!

Question: How do you write maths directly with correct notation here? I have to take pics of my work and then upload the pics.
 
yakin said:
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Question: How do you write maths directly with correct notation here? I have to take pics of my work and then upload the pics.

We have $\LaTeX$ implemented here to allow writing mathematical expressions.

Here is a link to a thread containing a pdf tutorial written by one of our staff:

http://mathhelpboards.com/latex-tips-tutorials-56/math-help-boards-latex-guide-pdf-1142.html
 

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