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. 1) 2)
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#1: 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 so 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?.
for all Since we have that the sequence is constant ( that can be done by induction) So for all Summing: On the LHS we have a telescoping sum: Cancelling out the terms: So:
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