2 - Ma116 Name E-Mail Exam II ID Lecturer I pledge my honor...

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Ma116 Exam II 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 → ∞ . 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 → ∞ ? 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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2 Let f ( x ) be a function defined for x 1 . Consider the series X n = 1 [ f ( n + 1 ) - f ( n ) ] ( * ) a [10 pts] Find a simple expression for S k , the kth partial sum associated with ( * ) . b [6 pts.] Suppose lim x →∞ f ( x ) = - 3 and f ( 1 ) = 4 . What does ( * ) converge to?
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3 Test the following series for convergence or divergence. Be sure to indicate what test or tests you use to arrive at your conclusions. a [8 pts.] X n = 1 ( - 1 ) n n 9 b [8 pts.]
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