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Math21CDisc9

# Math21CDisc9 - Math 210 Kouba Discussion Sheet 9 1...

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Unformatted text preview: Math 210 Kouba Discussion Sheet 9 1.) Determine conVrergence or divergence of each series using the test indicated. I suggest that you read all of the assumptions and conclusions for each test from the handout I gave last time as you do% each problem‘ n~1 n3 0; 7 c ) Z(—1)"+1 2 3 (Use the alternating series test.) n n=1 1 ‘1 1 l 1 1 l 1 d.) 1+ — — ~— + — + —— — — + — + — — —— + (Use the absolute conver— e.) Z(—1)"(l/10) (Use the sequence of partial sums test.) 11.20 00 f.) 2 (Use the limit comparison test.) n=1 2.) Use a geometric series to convert the decimal number 0.777777777... to a fraction. 00 1 3. The series — diver es. ) n; n g a.) Use equation to determine between which two numbers the partial sum 50 1 S50 2 Z lies. i=1 n 1 b.) What should n be in order that the partial sum 5' : Z —. be at least 20 ? 1 i=1 ” 1 C.) What is the largest value of n for which the partial sum Sn 2 Z does not i=1 exceed 50 ? Tl ' 00 4.) 1e series E converges. _ ‘ 5 1 a.) Compute the partial sum S5 = E 3. Use to estimate the resulting error. 7, i=1 17. 1 b.) What should n be in order that the partial sum 5' = Z 3 estimate the exact 2 i=1 value of the series with error at most 0.0001 ? 00 1 5.) The alternating; series Z(~1)"+17—13 converges. n=1 5 . 1 . a.) Compute the partial sum 5'5 : E (—1)‘+1,—3—. Estimate the resulting absolute 2 i=1 error. Between what two numbers does the exact value of the series lie ? n . 1 b.) What should 7?. be in order that the partial sum Sn : :(—1)’+1i—3 estimate the i=1 exact value of the series with absolute error at most 0.0001 ? “What is important is to keep learning, to enjoy challenge, and to tolerate ambiguity. In the end there are no certain answers.” — Martina Horner ...
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• Spring '09
• Kouba
• Math, Calculus, Mathematical Series, Partial sum, Martina Horner

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