{"id":127819,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/matrix-series-methods-comparison-tests"},"modified":"2017-08-16T06:22:46","modified_gmt":"2017-08-16T06:22:46","slug":"matrix-series-methods-comparison-tests","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/matrix-series-methods-comparison-tests\/","title":{"rendered":"Matrix &#038; Series Methods ( Comparison Tests )"},"content":{"rendered":"<div class=\"the_content_wrapper\">\n<p>Matrix &amp; Series Methods ( Comparison Tests )<br \/> Saeed Almheiri MTH306JohnsonS17<br \/> Assignment Comparison Tests due 05\/22\/2017 at 11:59pm PDT<br \/> 1. (1 point) Determine whether the following series converges<br \/> or diverges.<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> 7<br \/> 6+4<br \/> n<br \/> Input C for convergence and D for divergence:<br \/> Note: You have only one chance to enter your answer.<br \/> Answer(s) submitted:<br \/> \u2022<br \/> (incorrect)<br \/> 2. (1 point) Determine whether the following series converges<br \/> or diverges:<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> n<br \/> \u221a<br \/> n<br \/> 6 +2<br \/> Input C for convergence and D for divergence:<br \/> Note: You have only one chance to enter your answer.<br \/> Answer(s) submitted:<br \/> \u2022<br \/> (incorrect)<br \/> 3. (1 point) Match each of the following with the correct<br \/> statement.<br \/> C stands for Convergent, D stands for Divergent.<br \/> 1.<br \/> \u221e<br \/> \u2211<br \/> n=3<br \/> 6<br \/> n<br \/> 5 \u221249<br \/> 2.<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> 7+4<br \/> n<br \/> 6+1<br \/> n<br \/> 3.<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> ln(n)<br \/> 5n<br \/> 4.<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> 6<br \/> n(n+2)<br \/> 5.<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> 1<br \/> 6+<br \/> \u221a2<br \/> n<br \/> 6<br \/> Answer(s) submitted:<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> (incorrect)<br \/> 4. (1 point) Each of the following statements is an attempt<br \/> to show that a given series is convergent or divergent using the<br \/> Comparison Test (NOT the Limit Comparison Test.) For each<br \/> statement, enter C (for \u201dcorrect\u201d) if the argument is valid, or<br \/> enter I (for \u201dincorrect\u201d) if any part of the argument is flawed.<br \/> (Note: if the conclusion is true but the argument that led to it<br \/> was wrong, you must enter I.)<br \/> 1. For all n &gt; 1, n<br \/> 6\u2212n<br \/> 3 &lt;<br \/> 1<br \/> n<br \/> 2<br \/> , and the series \u2211<br \/> 1<br \/> n<br \/> 2 converges,<br \/> so by the Comparison Test, the series \u2211<br \/> n<br \/> 6\u2212n<br \/> 3 converges.<br \/> 2. For all n &gt; 1, arctan(n)<br \/> n<br \/> 3 &lt;<br \/> \u03c0<br \/> 2n<br \/> 3<br \/> , and the series \u03c0<br \/> 2 \u2211<br \/> 1<br \/> n<br \/> 3 converges,<br \/> so by the Comparison Test, the series \u2211<br \/> arctan(n)<br \/> n<br \/> 3<br \/> converges.<br \/> 3. For all n &gt; 2, ln(n)<br \/> n<br \/> 2 &gt;<br \/> 1<br \/> n<br \/> 2<br \/> , and the series \u2211<br \/> 1<br \/> n<br \/> 2 converges,<br \/> so by the Comparison Test, the series \u2211<br \/> ln(n)<br \/> n<br \/> 2 converges.<br \/> 4. For all n &gt; 1, ln(n)<br \/> n<br \/> 2 &lt;<br \/> 1<br \/> n<br \/> 1.5<br \/> , and the series \u2211<br \/> 1<br \/> n<br \/> 1.5 converges,<br \/> so by the Comparison Test, the series \u2211<br \/> ln(n)<br \/> n<br \/> 2<br \/> converges.<br \/> 5. For all n &gt; 2, 1<br \/> n<br \/> 2\u22121<br \/> &lt;<br \/> 1<br \/> n<br \/> 2<br \/> , and the series \u2211<br \/> 1<br \/> n<br \/> 2 converges,<br \/> so by the Comparison Test, the series \u2211<br \/> 1<br \/> n<br \/> 2\u22121<br \/> converges.<br \/> 6. For all n &gt; 2, n<br \/> n<br \/> 3\u22125<br \/> &lt;<br \/> 2<br \/> n<br \/> 2<br \/> , and the series 2\u2211<br \/> 1<br \/> n<br \/> 2 converges,<br \/> so by the Comparison Test, the series \u2211<br \/> n<br \/> n<br \/> 3\u22125<br \/> converges.<br \/> Answer(s) submitted:<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> (incorrect)<br \/> 5. (1 point) The three series \u2211An, \u2211Bn, and \u2211Cn have terms<br \/> An =<br \/> 1<br \/> n<br \/> 7<br \/> , Bn =<br \/> 1<br \/> n<br \/> 4<br \/> , Cn =<br \/> 1<br \/> n<br \/> .<br \/> Use the Limit Comparison Test to compare the following series<br \/> to any of the above series. For each of the series below, you<br \/> must enter two letters. The first is the letter (A,B, or C) of the<br \/> series above that it can be legally compared to with the Limit<br \/> Comparison Test. The second is C if the given series converges,<br \/> or D if it diverges. So for instance, if you believe the series<br \/> converges and can be compared with series C above, you would<br \/> enter CC; or if you believe it diverges and can be compared with<br \/> series A, you would enter AD.<br \/> 1<br \/> 1.<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> 4n<br \/> 4 +n<br \/> 7<br \/> 1309n<br \/> 11 +8n<br \/> 4 +4<br \/> 2.<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> 4n<br \/> 3 +n<br \/> 2 \u22124n<br \/> 8n<br \/> 10 \u22124n<br \/> 9 +7<br \/> 3.<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> 4n<br \/> 2 +4n<br \/> 6<br \/> 4n<br \/> 7 +8n<br \/> 3 \u22124<br \/> Answer(s) submitted:<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> (incorrect)<br \/> 6. (1 point) The series<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> n<br \/> k<br \/> r<br \/> n<br \/> converges when 0 &lt; r &lt; 1 and<br \/> diverges when r &gt; 1. This is true regardless of the value of the<br \/> constant k. When r = 1 the series is a p-series. It converges if<br \/> k &lt; \u22121 and diverges otherwise. Each of the series below can be<br \/> compared to a series of the form<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> n<br \/> k<br \/> r<br \/> n<br \/> . For each series determine<br \/> the best value of r and decide whether the series converges.<br \/> A.<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> (3+n(7)<br \/> n<br \/> )<br \/> \u22125<br \/> r = converges or diverges (c or d)?<br \/> B.<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> n<br \/> \u03c0<br \/> 5<br \/> 2n<br \/> 5<br \/> n +n<br \/> 9<br \/> r = converges or diverges (c or d)?<br \/> C.<br \/> \u221e<br \/> \u2211<br \/> n=1<br \/> n<br \/> .5 +4<br \/> n<br \/> 5 +7<br \/> r = converges or diverges (c or d)?<br \/> D.<br \/> \u221e<br \/> \u2211<br \/> n=1<\/p>\n<p>4n<br \/> 2 +5n+3<br \/> \u22128n<br \/> 6<br \/> n+9 +5n+7<br \/> \u221a<br \/> n<br \/> 8<br \/> r = converges or diverges (c or d)?<br \/> Answer(s) submitted:<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> (incorrect)<br \/> 7. (1 point) Use the limit comparison test to determine<br \/> whether<br \/> \u221e<br \/> \u2211<br \/> n=6<br \/> an =<br \/> \u221e<br \/> \u2211<br \/> n=6<br \/> 9n<br \/> 3 \u22124n<br \/> 2 +6<br \/> 4+2n<br \/> 4<br \/> converges or diverges.<br \/> (a) Choose a series<br \/> \u221e<br \/> \u2211<br \/> n=6<br \/> bn with terms of the form bn =<br \/> 1<br \/> n<br \/> p<br \/> and<br \/> apply the limit comparison test. Write your answer as a fully<br \/> simplified fraction. For n \u2265 6,<br \/> lim<br \/> n\u2192\u221e<br \/> an<br \/> bn<br \/> = lim<br \/> n\u2192\u221e<br \/> (b) Evaluate the limit in the previous part. Enter \u221e as infinity<br \/> and \u2212\u221e as -infinity. If the limit does not exist, enter DNE.<br \/> lim<br \/> n\u2192\u221e<br \/> an<br \/> bn<br \/> =<br \/> (c) By the limit comparison test, does the series converge, diverge,<br \/> or is the test inconclusive?<br \/> \u2022 Choose<br \/> \u2022 Converges<br \/> \u2022 Diverges<br \/> \u2022 Inconclusive<br \/> Answer(s) submitted:<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> \u2022<br \/> (incorrect)<br \/> Generated by c WeBWorK, http:\/\/webwork.maa.org, Mathematical Association of America<br \/> 2<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Matrix &amp; Series Methods ( Comparison Tests ) Saeed Almheiri MTH306JohnsonS17 Assignment Comparison Tests due 05\/22\/2017 at 11:59pm PDT 1. (1 point) Determine whether the following series converges or diverges. \u221e \u2211 n=1 7 6+4 n Input C for convergence <a href=\"https:\/\/www.benedictsol.com\/blogs\/matrix-series-methods-comparison-tests\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-127819","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/127819","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=127819"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/127819\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=127819"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=127819"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=127819"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}