Question 1:
This is a partial fraction decomposition.
7x+7/(x-8)^2
What I have so far is A/(x-8) + B/(x-8)^2
So far so good?? If I have gone about this correctly, I now have 7x+7 = A(x-8) + B. Now what do I do? What values do I plug in?
Question 2:
This sequence is defined recursively and I need to find the first 4 terms.
a(1) = y , {a(n)} = a(n-1) + u
Everything that's in parenthesis are subscripts. The first term is given, but what do I do with the y? How do I utilize it to find the next three terms?
I'm not asking for answers, but just some guidance. Thank you.
This is a partial fraction decomposition.
7x+7/(x-8)^2
What I have so far is A/(x-8) + B/(x-8)^2
So far so good?? If I have gone about this correctly, I now have 7x+7 = A(x-8) + B. Now what do I do? What values do I plug in?
Question 2:
This sequence is defined recursively and I need to find the first 4 terms.
a(1) = y , {a(n)} = a(n-1) + u
Everything that's in parenthesis are subscripts. The first term is given, but what do I do with the y? How do I utilize it to find the next three terms?
I'm not asking for answers, but just some guidance. Thank you.
-
1. 7x + 7 = A(x - 8) + B
Distribute A inside the parentheses on the right:
7x + 7 = Ax - 8A + B
A and B are constants, so the only term that can equal 7x has to have an x in it. Set the constant on the left equal to the constants on the right; your equations should be
7x = Ax
7 = -8A + B
For the second one, it seems like the second term would be y + u, the third term would be y + 2u, etc.
Distribute A inside the parentheses on the right:
7x + 7 = Ax - 8A + B
A and B are constants, so the only term that can equal 7x has to have an x in it. Set the constant on the left equal to the constants on the right; your equations should be
7x = Ax
7 = -8A + B
For the second one, it seems like the second term would be y + u, the third term would be y + 2u, etc.