Transcript
![Page 1: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/1.jpg)
![Page 2: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/2.jpg)
Empirijska indukcija
![Page 3: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/3.jpg)
![Page 4: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/4.jpg)
![Page 5: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/5.jpg)
![Page 6: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/6.jpg)
![Page 7: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/7.jpg)
Binomna formula𝑛! = 1 ∙ 2 ∙ 3 ∙ ⋯𝑛 čita se n –faktorijel
0! = 1 1! = 1 𝑛 + 1 ! = 𝑛! ∙ 𝑛 + 1
𝑛𝑘 - čita se n nad k I naziva binomni koeficijent za 0 ≤ 𝑘 ≤ 𝑛 definiše se sa
𝑛𝑘 =
𝑛 !
𝑘 !∙ 𝑛−𝑘 ! 𝑛
𝑘 =
𝑛∙ 𝑛−1 ∙⋯∙ 𝑛−𝑘+1
𝑘 !
Ako je 𝑘 > 𝑛 𝑛𝑘 = 0 𝑛
0 = 1 𝑛
𝑛 = 1 𝑛
1 = 𝑛
Stav: Ako je 𝑘 ≤ 𝑛 𝑘,𝑛 ∈ 𝑁 onda je
𝑛
𝑘 =
𝑛
𝑛 − 𝑘
𝑛
𝑘 − 1 +
𝑛
𝑘 =
𝑛 + 1
𝑘
![Page 8: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/8.jpg)
Binomni koeficijent Primer:
![Page 9: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/9.jpg)
![Page 10: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/10.jpg)
Primer: Razviti binom:
Rešenje: Po binomnoj formuli je
![Page 11: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/11.jpg)
Paskalov trougao
![Page 12: Empirijskaindukcija...BINOMNA FORMULA Binomna formula glasi: 1b + n a b n ab + 1 n n a b n 10 10 Title Matematička indukcija Author Dragan Created Date 10/22/2020 3:34:59 PM](https://reader033.vdocuments.pub/reader033/viewer/2022053115/60906b86ab5d1052a56d9bb6/html5/thumbnails/12.jpg)
Paskalov trougao