discrete mathematic

question 4,5 and 6

Problem 4 (1pt): Prove that the following set A is countable: A consists of all infinite sequences a0,a1, that are monotone and such that for every i=0,1,,ai{0,1,2}. Problem 5 (3 pts): Find the limits of the following sequences (show your work, explain your reasoning; you may use properties discussed in class) (a) limnn+13n/2 (b) limnn+1log5(3n2+2) (c) limnn+1n22n+4 (e) limnn+1n+log3(n+1) (f) limn+n2+12log3n Problem 6(1pt) : Use mathmatical induction to prove that n2n ! holds for every n4