{"id":353,"date":"2012-05-13T17:53:02","date_gmt":"2012-05-13T21:53:02","guid":{"rendered":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/?p=353"},"modified":"2012-05-13T17:53:02","modified_gmt":"2012-05-13T21:53:02","slug":"math-7a-lesson-12-5132012","status":"publish","type":"post","link":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/2012\/05\/13\/math-7a-lesson-12-5132012\/","title":{"rendered":"Math 7A, Lesson 12, 5\/13\/2012"},"content":{"rendered":"<p>Today we are onto geometric series, which talks about the sum of the first n terms of a geometric sequence. Given a geometric seuqnece with a as its first term, and r as its common ratio, the sum of its first n terms can be written as:<\/p>\n<p>Sn = a(r^n &#8211; 1)\/(r-1)<\/p>\n<p>We talk about whether a series is convergent (which means the sum is bounded by a constant), or divergent (the series always go bigger or smaller), or it is un-determinant.<\/p>\n<p>When r &gt; 1, the series is divergent;<\/p>\n<p>When r = 1, it is a constant sequence, Sn = a*n, so it is divergent;<\/p>\n<p>When -1 &lt; r &lt; 1, or |r| &lt; 1, the series converges to a\/(1-r);<\/p>\n<p>When r = -1, the series jumps between 0 and a, so it is undeterminant;<\/p>\n<p>When r &lt; -1, the series jumps between positive and negative, so it is also undeterminant.<\/p>\n<p>The homework is as follows:<\/p>\n<p><a href=\"http:\/\/www.newtonchineseschool.org\/teachers\/wangweidong\/HomeworkGeometricSeries.pdf\" target=\"_blank\"><span style=\"font-size: small\">http:\/\/www.newtonchineseschool.org\/teachers\/wangweidong\/HomeworkGeometricSeries.pdf<\/span><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Today we are onto geometric series, which talks about the sum of the first n terms of a geometric sequence. Given a geometric seuqnece with a as its first term, and r as its common ratio, the sum of its first n terms can be written as: Sn = a(r^n &#8211; 1)\/(r-1) We talk about [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[4,10,3],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/353"}],"collection":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/comments?post=353"}],"version-history":[{"count":2,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/353\/revisions"}],"predecessor-version":[{"id":356,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/353\/revisions\/356"}],"wp:attachment":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/media?parent=353"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/categories?post=353"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/tags?post=353"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}