{"id":5,"date":"2016-09-29T23:28:55","date_gmt":"2016-09-30T06:28:55","guid":{"rendered":"https:\/\/blogs.ubc.ca\/qiwei\/?p=5"},"modified":"2016-09-29T23:28:55","modified_gmt":"2016-09-30T06:28:55","slug":"assignment-3-q3","status":"publish","type":"post","link":"https:\/\/blogs.ubc.ca\/qiwei\/2016\/09\/29\/assignment-3-q3\/","title":{"rendered":"Assignment 3 Q3"},"content":{"rendered":"<p>a) what distinguishes convergent sequence from divergent sequences<br \/>\n  When n is approaching to the infinity, the convergent sequence is close to a real number not approaching to the infinity. For example, the sequence {1\/n}, in this sequence, when n is approaching to the infinity, 1\/n is approaching to 0.<br \/>\n  When n is approaching to the infinity, the divergent sequences do not approach to any real number or approach to the infinity, For example 1) {(-1)^n}, in this sequence, we cannot figure out what is the data when n is approaching to the infinity, it can be 1 or -1.  2) {n^2}, in this sequence, when n is approaching to the infinity, the sequence is approaching to the infinity as well.<\/p>\n<p>b) what distinguishes convergent series from divergent series.<br \/>\n  Convergent series is the sum of the sequence is close to a number. From the ratio rule, when the |r|< 1 in a series, this series is convergent. For example, the series{1\/(n^2)}\n  Divergent series is the sum of the sequence is close to the infinity. From the ratio rule, when the |r|> 1 is a series, this series is divergent. For example, the series {2^n}.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>a) what distinguishes convergent sequence from divergent sequences When n is approaching to the infinity, the convergent sequence is close to a real number not approaching to the infinity. For example, the sequence {1\/n}, in this sequence, when n is approaching to the infinity, 1\/n is approaching to 0. When n is approaching to the [&hellip;]<\/p>\n","protected":false},"author":44838,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-5","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/qiwei\/wp-json\/wp\/v2\/posts\/5","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/qiwei\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/qiwei\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/qiwei\/wp-json\/wp\/v2\/users\/44838"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/qiwei\/wp-json\/wp\/v2\/comments?post=5"}],"version-history":[{"count":1,"href":"https:\/\/blogs.ubc.ca\/qiwei\/wp-json\/wp\/v2\/posts\/5\/revisions"}],"predecessor-version":[{"id":7,"href":"https:\/\/blogs.ubc.ca\/qiwei\/wp-json\/wp\/v2\/posts\/5\/revisions\/7"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/qiwei\/wp-json\/wp\/v2\/media?parent=5"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/qiwei\/wp-json\/wp\/v2\/categories?post=5"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/qiwei\/wp-json\/wp\/v2\/tags?post=5"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}