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16c_m3_S02_condenced

# 16c_m3_S02_condenced - AMTH 16C TEST 3 Spring 2002 1 18 pts...

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AMTH 16C TEST 3 Spring 2002 1.( 18 pts) Assume that X n =1 a n is a convergent series , and X n =1 b n is a divergent series. Let X n =1 c n be a series with partial sums S k . Indicate the convergence or divergence of X n =1 c n by putting C for convergence , D for divergence and N for no conclusion can be made in the blank space provided for each part. i) 0 < c n < b n .............. ii) 0 < c n < a n .............. iii) 0 < a n < c n .............. iv) 0 < b n < c n .............. v) lim n →∞ S n = 5 .............. vi) lim n →∞ S n = .............. vii) lim n →∞ c n = 0 .............. viii) lim n →∞ c n = 1 .............. ix) lim n →∞ c n = 1 2 .............. x) lim n →∞ c n = 2 .............. xi) lim n →∞ c n +1 c n = 1 2 .............. xii) lim n →∞ c n +1 c n = 0 .............. xiii) lim n →∞ c n +1 c n = 2 .............. xiv) lim n →∞ c n +1 c n = 1 .............. xv) lim n →∞ a n c n = 2 .............. xvi) lim n →∞ a n c n = 0 .............. xvii) lim n →∞ b n c n = 2 .............. xviii) lim n →∞ c n b n = 0 .............. 2. (15 pts.) Use a sixth degree taylor Polynomial centered at c = 0 to approximate Z 1 4 0 ln( x 2 + 1) dx . 3. (10pts.) Approximate 1 3 e using the first 3 nonzero term of a maclaurian series. 4. (27 pts.) Determine if the following series converge or diverge, justify your answer. a. (7 pts.) X n =1 1 1 + e - n b. (5 pts.) X n =1 12 n c. (8 pts.) X n
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