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İkinci bölümde ise aritmetik dizilerde terimler arası fark, artış miktarı ve toplam formülleri detaylı olarak anlatılmaktadır.","Video sonunda eğitmen, izleyicilere 1'den n'ye kadar olan sayıların karelerinin toplamının formülünü tüme varım yöntemiyle göstermelerini ödev olarak vermektedir."]},"endTime":620,"title":"Tüme Varım Metodu ile Toplam Formülleri","beginTime":0}],"fullResult":[{"index":0,"title":"Tüme Varım Yöntemi ve Ödev","list":{"type":"unordered","items":["Geçen videoda, 1'den n'ye kadar olan doğal sayıların toplamının n×(n+1)/2 formülüyle hesaplandığını tüme varım yöntemiyle ispatlamak ödevi verilmişti.","Tüme varım yöntemi, bir formülün aldığımız her değer için sağlandığını göstererek, tüm değerler için geçerli olduğunu kanıtlama yöntemidir.","Bu videoda tüme varım yöntemi kullanılarak ödevin çözümü gösterilecek ve sonunda yeni bir ödev bırakılacaktır."]},"beginTime":0,"endTime":44,"href":"/video/preview/4134622419284279170?parent-reqid=1765135123466059-16882299653655514018-balancer-l7leveler-kubr-yp-klg-219-BAL&text=N+++1&t=0&ask_summarization=1"},{"index":1,"title":"Tüme Varım Yönteminin Uygulanması","list":{"type":"unordered","items":["İspat için önce n=1 ve n=2 değerleri için formülün doğruluğu kontrol edilir: 1'den 1'e kadar toplam 1, formülde 1×2/2=1; 1'den 2'ye kadar toplam 3, formülde 2×3/2=3 olarak hesaplanır.","Keyfi bir k değeri için formülün doğru kabul edilir: 1'den k'ye kadar toplam k×(k+1)/2 olarak varsayılır.","Bu varsayımdan sonra, k+1 değeri için formülün de doğru olduğu gösterilir: 1'den k+1'e kadar toplam k×(k+1)/2 + (k+1) = (k+1)×(k+2)/2 olarak hesaplanır."]},"beginTime":44,"endTime":233,"href":"/video/preview/4134622419284279170?parent-reqid=1765135123466059-16882299653655514018-balancer-l7leveler-kubr-yp-klg-219-BAL&text=N+++1&t=44&ask_summarization=1"},{"index":2,"title":"Sonuç ve Ek Bilgi","list":{"type":"unordered","items":["Tüme varım yöntemiyle 1'den n'ye kadar olan sayıların toplamının n×(n+1)/2 formülüyle hesaplandığı ispatlanmıştır.","Bu toplam formülü aslında aritmetik dizilerde toplam hesaplamak için kullanılır.","Aritmetik dizi, artış miktarı değişmeden artan ifadelerin dizisidir ve örneğin 1, 4, 7, 10 gibi 3'er 3'er artan bir dizi de aritmetik dizidir."]},"beginTime":233,"endTime":269,"href":"/video/preview/4134622419284279170?parent-reqid=1765135123466059-16882299653655514018-balancer-l7leveler-kubr-yp-klg-219-BAL&text=N+++1&t=233&ask_summarization=1"},{"index":3,"title":"Aritmetik Dizilerde Artış Miktarı","list":{"type":"unordered","items":["Aritmetik dizilerde tüm terimler arası fark aynıdır, örneğin 1234 dizisinde fark 1'dir.","Birinci ile üçüncü terim toplanıp ikiye bölüldüğünde veya üçüncü terimden birinci terim çıkarılıp ikiye bölüldüğünde artış miktarı bulunur.","Herhangi bir terimden ilk terim çıkarılıp terim sayısının farkı ile bölündüğünde de 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squeeze theorem to prove lim n^(1/n) = 1. Thanks for watching!! ❤️ // my other squeeze theorem video: • [Proof] lim (a^n + b^n)^(1/n) = b | Squeez... Tip Jar 👉🏻👈🏻 ☕...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2840949/c94f5e1a8da78cd5b95dfcf887fe452c/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/jzRSEQEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"10","reqid":"1765135123466059-16882299653655514018-balancer-l7leveler-kubr-yp-klg-219-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DicEKOKNAYtQ","linkTemplate":"/video/preview/9984298497167800617?parent-reqid=1765135123466059-16882299653655514018-balancer-l7leveler-kubr-yp-klg-219-BAL&text=N+++1&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"[Proof] lim n^(1/n) = 1 | Squeeze Theorem","related_orig_text":"N 1","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"N 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Öğretmen, 4 Mayıs tarihinde 5N1K konusunu anlatmaktadır.","Videoda 5N1K sorularının ne olduğu, \"kim\", \"ne\", \"nerede\", \"nasıl\", \"neden/niçin\" ve \"ne zaman\" sorularını içeren bu soruların cümlelerde nasıl kullanılacağı örneklerle açıklanmaktadır. Öğretmen, altı çizili sözcüklerin hangi 5N1K sorusunun cevabı olduğunu bulma sorusunu çözerek konuyu pekiştirmektedir.","Video, ödevlerin yapılması ve ödüllü soruya cevap verilmesi çağrısıyla sonlanmaktadır. 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this math video lesson on Solving Rational Equations I solve the equation 1/n=1/5n-(n-1)/5n. 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