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Howework: Solving Rerusions Solve the following recursions: 1. al = 2, and an-an-1 + 2, for n > 1. 2, al = 3, and an = an-1 + n, for n > 1. 3. a-4, and an -3an-1+1, for n>0 4.ao 2, and an = 2 * an-1 + 10, for n > 0. 5, al = c, and an-an-1 + b, for n > 0. 6. It is a tradition in your club for a new member to shake hands with each of the current members. Suppose the club starts with one member and new members are introduced one at a time. Find a recusion for determining the total number of handshakes made when the club has n members. Solve this recusion, and prove your answer. How many handshakes are made if membership grows to 100? 7. There is a muyth of Buddhist monks in heaven solving this puzzle with 100 golden disks on three silver pegs. They make one move a second and the claim is that when they finish the puzzle, the world will end. Scientist agree that the Earth is about 4.5 billion years old. Suppose this myth is correct. When will the world end