{"id":125464,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/calculus-series-2"},"modified":"2017-08-16T06:04:26","modified_gmt":"2017-08-16T06:04:26","slug":"calculus-series-2","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/calculus-series-2\/","title":{"rendered":"Calculus Series"},"content":{"rendered":"<div class=\"the_content_wrapper\">\n<p>Calculus Series<\/p>\n<p>1. Show that if 0 S 51? S 1\/2 then -2:17 S ln(1 \u2013 T) S -1?. Suggestion: Let<br \/> f(:17) : ln(1-:17). show that its first derivative is decreasing. calculate possible<br \/> derivative values for the X in question. invoke the l~\u201clean Value Theorem.<br \/> 2. Given a sequence an. Where each 0 S an S 1\/2. form the infinite product<br \/> 00<br \/> W1 \u2013 an)<br \/> 71:1<br \/> Each term in the product is between 0 and 1. so the partial products are<br \/> monotone decreasing. Using the result of the first problem. show that<br \/> 00 00<br \/> H&lt;1 _ (1\/71) 2 0 fi 5 (1\/71 2 00 71:1 71:1 3. (Deep thinking for this one) Suppose that the positive series 2 an con- verges. Define bit 2 (Lg-H That is. 1\/2 2\/3 3\/4 blzal b2:a2 b3:a3 Prove that 2 bn must converge. Hint: find an upper bound for the partial sums. <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Calculus Series 1. Show that if 0 S 51? S 1\/2 then -2:17 S ln(1 \u2013 T) S -1?. Suggestion: Let f(:17) : ln(1-:17). show that its first derivative is decreasing. calculate possible derivative values for the X in question. <a href=\"https:\/\/www.benedictsol.com\/blogs\/calculus-series-2\/\" 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-125464","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/125464","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=125464"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/125464\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=125464"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=125464"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=125464"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}