I don't realy understand how to solve recurrence relations. I have the following 2 problems and I don't know how to work them.
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We get the quadratic:
Solve the system and we get:
Can you get the other?. It has 1 as a root of multiplicity 2, so you will need an extra n:
So for number 2:
a * 1^0 + b*(0)*1^0 = 4
a = 4
a*1^1 + b(1) * 1^1 = 1
5 + b = 1
b = -4
4 * 2^n - 4 * 1^n
This works for a_0 but not a_1. Where did I go wrong. By the way, thanks so much. Trying to do this on my own and its hard!
The solution(s) is 1 and 1. Remember, I said multiplicity 2?.
Since we have that the sequence is constant ( that can be done by induction)
So for all
On the LHS we have a telescoping sum:
Cancelling out the terms:
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