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9- MAVZU

9- MAVZU. Nyuton binomi. Polinomial formula. Kiritish va Chiqarish usuli. Rekurent munosabatlar. REJA:. Nyuton binomi. Polinomial formula. Kiritish va chiqarish usuli. Rekurent munosabatlar. Мактаб курсидан маълумки (а + b ) 2 = а 2 +2а b + b 2 , (а+ b ) 3 =а 3 +3а 2 b +3а b 2 + b 3

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9- MAVZU

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  1. 9-MAVZU Nyuton binomi. Polinomial formula. Kiritish va Chiqarish usuli. Rekurent munosabatlar.

  2. REJA: • Nyuton binomi. • Polinomial formula. • Kiritish va chiqarish usuli. • Rekurent munosabatlar.

  3. Мактаб курсидан маълумки • (а +b)2= а2+2аb+b2, • (а+b)3=а3+3а2b+3аb2+b3 • Бу формулаларни умумлаштириб (а+b)nкавсни кандай очиш мумкин деган савол туғулиши табиийдир. Бу саволга қуйидаги теорема жавоб беради:

  4. Teorema (Binomial teorema) Quyidagi tenglik o‘rinli • bu yerda sonlarga binomial koeffitsiyentlar, tenglamaga esa Nyuton binomi deyiladi.

  5. Ushbu nom tarixiy haqiqat emas, chunki Nyutondan oldin ushbu formulani Umar Xayyom (1046-1131), G‘iyos ad-Din Jamshid al-Koshi bilishgan. Nyutonning xizmati ushbu formulani butun bo‘lmagan nuchun umumlashtirgan.

  6. Polinomial teorema. ifoda, bo‘lishi mumkin bo‘lgan barcha quyidagi ko‘rinishdagi qo‘shiluvchilar yig‘indisidan iborat bo‘lib • Bu erda ,ya’ni • ga teng bo‘ladi.

  7. k=2 бўлганда (3) тенгликқуйидагикўринишгакелади : • Демак, хусусий холда Ньютон биноми формуласига эга бўламиз.

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