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Key test 3 sp'10

# Key test 3 sp'10 - 6 a L 00-n 72-S-n-4-n=O 4 Test for...

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Math 112 Test 3 PLEDGED~L:::::.::::::::!:::::::~L ___ _ Spring, 2010 Use your own paper, put a" problems in order, be neat and clear with your work. 1. Proofs: (12 points each) a) A geometric series, L ~ a"r" with ratio of r, converges if Irl < 1 with sum of -- a . ,,=0 l-r b) State and prove the nth term test. 2. Sequence: (12 points) Given: an = cos( : ) a) Give the first four terms. b) Sketch the graph. c) Does the sequence, {an} converge? Explain your reasoning. 3. Find the sum or explain why the series is

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Unformatted text preview: 6 a) L 00 -n 72-+-S-n-+-4-n=O 4. Test for convergence. Clearly state your argument. If appropriate, tell whether the convergence is conditional or absolute. (12 points each, 60 points) a) f (-1)"2n n! n=1 [2·S·g···(3n-1)] c) f Arc tan( 4n) n=1 n ~ 2k e) L-k-k=l e -k lQ)~ ?k~~ ,--e (, ;J b) -n#l~ S l\~e d:; Q" = Cos (~ '), " = \} :?} 3 · · , b) Q.) Q\'= c-ostrr)= -1 Q.1 = CoS (n = 0 Q,3::: C.os (!") == ~ 0" -. Ott ::: CoS ({f') = 1f -I (~-I) f\\ "Y\= I s-. ) 'f= ~ d/l/~...
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Key test 3 sp'10 - 6 a L 00-n 72-S-n-4-n=O 4 Test for...

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