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2-ans - Ma116 Name E-Mail Exam II Solutions ID Lecturer I...

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Ma116 Exam II – Solutions 2/29/00 Name: ID: E-Mail: 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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