{"id":491,"date":"2009-02-17T01:47:49","date_gmt":"2009-02-16T23:47:49","guid":{"rendered":"http:\/\/www.umitcanli.com\/school\/?p=491"},"modified":"2025-05-31T15:18:47","modified_gmt":"2025-05-31T13:18:47","slug":"11-sinif-toplam-sembolu-calisma-kagidi-i","status":"publish","type":"post","link":"http:\/\/www.umitcanli.com\/school\/index.php\/2009\/02\/17\/11-sinif-toplam-sembolu-calisma-kagidi-i\/","title":{"rendered":"11. S\u0131n\u0131f Toplam Sembol\u00fc \u00c7al\u0131\u015fma K\u00e2\u011f\u0131d\u0131 I"},"content":{"rendered":"<p>Bilindi\u011fi \u00fczere, &#8220;toplam&#8221; sembol\u00fc ile \u00e7ok say\u0131daki terimin toplam\u0131 k\u0131sa olarak ifade edilebiliyor. Sonlu ve sonsuz dizi veya bunlar\u0131n toplam\u0131 olan serilerle u\u011fra\u015f\u0131rken s\u0131k\u00e7a kullan\u0131l\u0131yor olan toplam sembol\u00fc \u03a3<!--more-->, Yunan alfabesinin, \u03b1 \u03b2 veya \u03c8\u00a0gibi harflerinden biri. Bir seri veya diziyi ifade ederken, her bir terimi tamsay\u0131ya ba\u011fl\u0131 bir fonksiyon olarak ifade edebilmek isteriz. \u00c7al\u0131\u015fma k\u00e2\u011f\u0131d\u0131n\u0131n B grubundaki sorular buna dair. Her biri birer bilmece tad\u0131nda da g\u00f6r\u00fclebilir. A b\u00f6l\u00fcm\u00fcndeki sorular, bir dizideki terim say\u0131s\u0131n\u0131 bulmaya y\u00f6nelik. Di\u011fer a\u00e7\u0131klamalar ve sorular da, muhtemelen unutmu\u015f olabilece\u011finiz Binom a\u00e7\u0131l\u0131m\u0131, bununla ba\u011flant\u0131l\u0131 olarak Pascal \u00dc\u00e7geni ile ilgili. Sona do\u011fru g\u00f6r\u00fcyor olaca\u011f\u0131n\u0131z iki adet \u00e7arpanlara ay\u0131rma kural\u0131 sayesinde, (daha sonra) a\u015fa\u011f\u0131daki soru \u00fczerine kafa yorabiliyor veya cebirsel bir yorum getirebiliyoruz:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"http:\/\/www.umitcanli.com\/content\/images\/mixed\/steps.gif\" alt=\"\" width=\"206\" height=\"41\" \/><\/p>\n<p>Asl\u0131nda bu soru, <a href=\"http:\/\/tr.wikipedia.org\/wiki\/Eleal\u0131_Zeno\" target=\"_blank\">Zeno<\/a> paradoksunun basitle\u015ftirilmi\u015f hali ve \u015f\u00f6yle de \u00f6zetlenebilir:<\/p>\n<blockquote><p>Toplam olarak \u0130ki birimden olu\u015fan bir yolunuz var. (Say\u0131 do\u011frusunu d\u00fc\u015f\u00fcn\u00fcn&#8230;) Bu yolda ilerlemenin kurallar\u0131 \u015funlar:<\/p>\n<ul>\n<li>\u00d6nce bir birim ilerlenecek<\/li>\n<li>Sonraki her ad\u0131m\u0131n\u0131z, \u00f6nceki ad\u0131m\u0131n yar\u0131s\u0131 olacak.<\/li>\n<\/ul>\n<p>Bu bi\u00e7imde, 2 birimlik yolu y\u00fcr\u00fcyebilir misiniz ? Yani yolun sonuna ula\u015f\u0131labilir mi ?\u00a0<\/p><\/blockquote>\n<p>Bir di\u011fer deyi\u015fle, &#8220;Bu toplam 2&#8217;ye e\u015fit midir, yoksa 2&#8217;ye \u00e7ok mu yakla\u015f\u0131r ?&#8221;<\/p>\n<p>\u00dczerine kafa yorulabilecek ve zihin a\u00e7\u0131c\u0131 etki yapan sorulardan biridir bu. E\u011fer ilginizi \u00e7ekiyorsa, bu soru size; Daha \u00f6nce d\u00fc\u015f\u00fcnmemi\u015f oldu\u011funuzu fark edece\u011finiz bir \u00e7ok kavram\u0131 g\u00f6rme f\u0131rsat\u0131 verir. Bir ba\u015fka vakit daha da a\u00e7abiliriz bu konuyu. \u0130lginizi \u00e7ekiyorsa, bu ve biraz daha fazlas\u0131 i\u00e7in <a href=\"http:\/\/tr.wikipedia.org\/wiki\/Zeno'nun_paradokslar\u0131\" target=\"_blank\">\u015furaya<\/a> bir g\u00f6z atabilirsiniz.\u00a0<\/p>\n<p><a href=\"http:\/\/www.umitcanli.com\/content\/school\/11\/2008_2009_Sigma1.swf\" target=\"_blank\">Toplam Sembol\u00fc I &#8211; Flash Paper<\/a><\/p>\n<p><a href=\"http:\/\/www.umitcanli.com\/content\/school\/11\/2008_2009_Sigma1.pdf\" target=\"_blank\">Toplam Sembol\u00fc I &#8211; PDF<\/a><\/p>\n<p>Sorular\u0131 g\u00f6r\u00fcnt\u00fcleme veya \u00e7\u0131k\u0131\u015f alma ile ilgili problem ya\u015f\u0131yorsan\u0131z, <a href=\"http:\/\/www.umitcanli.com\/school\/index.php\/2007\/07\/10\/niye-yapamiyorum\/\">ilgili k\u0131s\u0131m<\/a> incelenebilir. \u0130yi \u00e7al\u0131\u015fmalar&#8230;<br \/>\n<span id=\"post-ratings-491\" class=\"post-ratings\" data-nonce=\"1e42862266\"><img decoding=\"async\" id=\"rating_491_1\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/stars\/rating_on.gif\" alt=\"1 Y\u0131ld\u0131z\" title=\"1 Y\u0131ld\u0131z\" onmouseover=\"current_rating(491, 1, '1 Y\u0131ld\u0131z');\" onmouseout=\"ratings_off(5, 0, 0);\" onclick=\"rate_post();\" onkeypress=\"rate_post();\" style=\"cursor: pointer; border: 0px;\" \/><img decoding=\"async\" id=\"rating_491_2\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/stars\/rating_on.gif\" alt=\"2 Y\u0131ld\u0131z\" title=\"2 Y\u0131ld\u0131z\" onmouseover=\"current_rating(491, 2, '2 Y\u0131ld\u0131z');\" onmouseout=\"ratings_off(5, 0, 0);\" onclick=\"rate_post();\" onkeypress=\"rate_post();\" style=\"cursor: pointer; border: 0px;\" \/><img decoding=\"async\" id=\"rating_491_3\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/stars\/rating_on.gif\" alt=\"3 Y\u0131ld\u0131z\" title=\"3 Y\u0131ld\u0131z\" onmouseover=\"current_rating(491, 3, '3 Y\u0131ld\u0131z');\" onmouseout=\"ratings_off(5, 0, 0);\" onclick=\"rate_post();\" onkeypress=\"rate_post();\" style=\"cursor: pointer; border: 0px;\" \/><img decoding=\"async\" id=\"rating_491_4\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/stars\/rating_on.gif\" alt=\"4 Y\u0131ld\u0131z\" title=\"4 Y\u0131ld\u0131z\" onmouseover=\"current_rating(491, 4, '4 Y\u0131ld\u0131z');\" onmouseout=\"ratings_off(5, 0, 0);\" onclick=\"rate_post();\" onkeypress=\"rate_post();\" style=\"cursor: pointer; border: 0px;\" \/><img decoding=\"async\" id=\"rating_491_5\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/stars\/rating_on.gif\" alt=\"5 Y\u0131ld\u0131z\" title=\"5 Y\u0131ld\u0131z\" onmouseover=\"current_rating(491, 5, '5 Y\u0131ld\u0131z');\" onmouseout=\"ratings_off(5, 0, 0);\" onclick=\"rate_post();\" onkeypress=\"rate_post();\" style=\"cursor: pointer; border: 0px;\" \/> (<strong>4<\/strong> ki\u015finin oyu ile <strong>5<\/strong> \u00fczerinden ortalama <strong>5,00<\/strong> verilmi\u015f)<\/span><span id=\"post-ratings-491-loading\" class=\"post-ratings-loading\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/loading.gif\" width=\"16\" height=\"16\" class=\"post-ratings-image\" \/>Loading...<\/span><\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_491\" class=\"pvc_stats all  \" data-element-id=\"491\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bilindi\u011fi \u00fczere, &#8220;toplam&#8221; sembol\u00fc ile \u00e7ok say\u0131daki terimin toplam\u0131 k\u0131sa olarak ifade edilebiliyor. Sonlu ve sonsuz dizi veya bunlar\u0131n toplam\u0131 olan serilerle u\u011fra\u015f\u0131rken s\u0131k\u00e7a kullan\u0131l\u0131yor olan toplam sembol\u00fc \u03a3<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_491\" class=\"pvc_stats all  \" data-element-id=\"491\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[93,3,2],"tags":[276,122,167,278,279,202,271,228,416,274,275,277,272,280,273],"class_list":["post-491","post","type-post","status-publish","format-standard","hentry","category-calisma-kagidi","category-matematik","category-okul","tag-276","tag-122","tag-2008-2009","tag-binom","tag-carpan","tag-fonksiyon","tag-gauss","tag-katsayi","tag-matematik","tag-pascal-ucgeni","tag-seri","tag-terim","tag-toplam-sembolu","tag-zeno","tag-273"],"a3_pvc":{"activated":true,"total_views":2070,"today_views":0},"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/pc2dpV-7V","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/posts\/491","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/comments?post=491"}],"version-history":[{"count":13,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/posts\/491\/revisions"}],"predecessor-version":[{"id":714,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/posts\/491\/revisions\/714"}],"wp:attachment":[{"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/media?parent=491"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/categories?post=491"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/tags?post=491"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}