{"id":12094,"date":"2015-09-01T16:13:21","date_gmt":"2015-09-01T16:13:21","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=12094"},"modified":"2018-02-13T18:53:14","modified_gmt":"2018-02-13T18:53:14","slug":"math-what-is-a-telescoping-sum","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-what-is-a-telescoping-sum\/","title":{"rendered":"Math:  what is a telescoping sum?"},"content":{"rendered":"<h1>The tutor gives brief coverage of a curiosity with polynomials.<\/h1>\n<p>Imagine expanding the product<\/p>\n<p>(1-x)(1+x+x^2+x^3)<\/p>\n<p>by multiplying, in turn, both terms from the first bracket by each one in the second:<\/p>\n<p>(1-x)(1+x+x^2+x^3)=1-x+x-x^2+x^2-x^3+x^3-x^4<\/p>\n<p>Note, in the expanded expression, the cancellation between the second and third terms, then between the  fourth and fifth, and so on.  The result is<\/p>\n<p>(1-x)(1+x+x^2+x^3)=1-x^4<\/p>\n<p>The cancellation between consecutive middle terms of the expansion makes it a telescoping sum.  I&#8217;ll be talking about implications of telescoping sums in future posts.:)<\/p>\n<p>Source:<\/p>\n<p>Grimaldi, Ralph P.  <u>Discrete and Combinatorial Mathematics<\/u>.  Addison-Wesley:  Toronto,<br \/>\u00a0\u00a0 1994.<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor gives brief coverage of a curiosity with polynomials. Imagine expanding the product (1-x)(1+x+x^2+x^3) by multiplying, in turn, both terms from the first bracket by each one in the second: (1-x)(1+x+x^2+x^3)=1-x+x-x^2+x^2-x^3+x^3-x^4 Note, in the expanded expression, the cancellation between &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-what-is-a-telescoping-sum\/\"> <span class=\"screen-reader-text\">Math:  what is a telescoping sum?<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-12094","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/12094","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=12094"}],"version-history":[{"count":16,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/12094\/revisions"}],"predecessor-version":[{"id":29635,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/12094\/revisions\/29635"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=12094"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=12094"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=12094"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}