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# Sheet7 - Math 21C DHC Kouba Discussion Sheet 7 1 Use any...

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Unformatted text preview: Math 21C DHC Kouba Discussion Sheet 7 1.) Use any method to test each of the following series for convergence or divergence. 0° 1 0° lnn 0° lnn 0° lnn 0° lnn 11:2 71:2 n22 n=2 n=2 00 Inn 2 0° Inn 3 0° (Inn)7 _ 0° 71” ﬂ) :E: ('22—) g) (”3?“) 1L) :2: n5 L) :2: 10nru 71:2 11:2 71:2 n=1 00 00 00 . 3W4an+1ﬂV +1n+8 mHn2+1 J) E: 7ﬂOQnﬂ k) E3i—Dn vﬁ—+1 I) §:('1) n2+8 71:1 11:2 n:1 w 2+M—n” 1 2 3 1 2 3 1 2 3 NEW n-)1§‘2—2+§+4—2‘5—2+6_2+7”2+‘33_9—2 +i+2+i+1 2+i+ 102 112 122 132 142 152 00 0° 2 0» 2W —1>" p» :w—(Zgﬁilzn2 77,21 71:]. . 1 n2+1 00 2.) The series 2 converges. What should n be in order that the partial sum 71:1 TL 1 Sn 2 2 estimate the exact value of the series with error at most 0.001 ? i=1 12 + 1 m 1 3.) The alternating series §:(—1)”+1 n2 + 1 converges. What should n be in order that n n=1 1 the partial sum S : Z:(—1)n+1 i2 + 1 estimate the exact value of the series with error i=1 at most 0.001 ? 4.) Use any method to test each of the following series for convergence or divergence. 00 n2 n 0" nn—H/n a.) ;(n2+1) b') T;(n+1/n)" ...
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