Calculus Series<\/p>\n
1. Show that if 0 S 51? S 1\/2 then -2:17 S ln(1 – T) S -1?. Suggestion: Let
\nf(:17) : ln(1-:17). show that its first derivative is decreasing. calculate possible
\nderivative values for the X in question. invoke the l~\ufffd\ufffd\ufffdlean Value Theorem.
\n2. Given a sequence an. Where each 0 S an S 1\/2. form the infinite product
\n00
\nW1 – an)
\n71:1
\nEach term in the product is between 0 and 1. so the partial products are
\nmonotone decreasing. Using the result of the first problem. show that
\n00 00
\nH<1 _ (1\/71) 2 0 fi 5 (1\/71 2 00\n71:1 71:1\n3. (Deep thinking for this one) Suppose that the positive series 2 an con-\nverges. Define\n\nbit 2 (Lg-H\nThat is.\n1\/2 2\/3 3\/4\nblzal b2:a2 b3:a3\nProve that 2 bn must converge. Hint: find an upper bound for the partial\nsums.\n\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"
Calculus Series 1. Show that if 0 S 51? S 1\/2 then -2:17 S ln(1 – 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. Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-6960","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/6960","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=6960"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/6960\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=6960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=6960"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=6960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}