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Question: i explain in words why each recurrence relation is represented...

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I. Explain in words why each recurrence relation is represented by the given description. 〔You do not need to solve the recurrence.) For example: H(2)=1 H(n)=H(n-1)+n-1 for n >3 H(n) is the number of handshakes in a room of n people where everybody shake hands with everybody else exactly once you could say: If there are two people in the room then there is only one handshake so P(2) 1 Lets say that I am one of the n people. We can divide the set of handshakes into two categories, the handshakes that I made and the handshakes that I did not make. I made n handshakes. The handshakes that I did not make were all the handshakes between the other 1 people as if I had not been there, so there are H(n -1) handshakes that I did not make. Therefore: H(n) - H(n 1)+n-1 C(0,C(2) 0, C(3) ,C(4)C(n) C(n -3) +C(n-4) for n2 5 C(n) is the number of sequences of 3s and 4s that add up to n. 13(1) = 2. B(2) = 4. B(3) = 7 B(n) = B(n-1) + B(n-2) + B(n-3) B(n) is the number of n-bit binary strings that avoid 000 for n > 3 F(1) 0 (n) 2F(n/2)+1 for n 2 1 F(n) is the number of matches played in a single elimination tournament with n players (you can assume n 2* for some positive integer k. You can use the bracket below to help explain.) 16 Team Single Eimination

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