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Unformatted text preview: Ma116 Exam II Solutions 2/29/00 Name: ID: EMail: Lecturer: I pledge my honor that I have abided by the Stevens Honor System. SHOW ALL WORK! You may not use a calculator on this exam. 1a [4 pts.] Let a n = ( 1 ) n n . Is the sequence { a n } convergent or divergent as n ? If it is convergent, then to what does it converge? If it is divergent, then what is the behavior of a n as n . Solution : lim n ( 1 ) n n = 0. 1b [4 pts.] Let a n = ( 1 ) n + 1 5 1 4 n . Is the sequence { a n } convergent or divergent as n ? If it is convergent, then to what does it converge? If it is divergent, then what is the behavior of a n as n ? Solution : If n is even, say n = 2 k , then lim n a 2 k =  5, whereas if n = 2 k + 1 is odd, lim n a n = 5. Thus the sequence diverges. 1c [4pts.] Let a n = 5 n 2 10 n + 2 1 2 n 2 . Is the sequence { a n } convergent or divergent as n ? If it is convergent, then to what does it converge? If it is divergent, then what is the behavior of a n as n ?...
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 Spring '08
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