Question

determine o 11 termo no desenvolvimento de (x-1)^20

Answer 1

$C_{11}^{20} = \dfrac{n!}{p! .(n - p)!} \\ \\ \\ C_{11}^{20} = -\dfrac{20!}{11! .(20 - 11)!} \\ \\ \\ C_{11}^{20} = -\dfrac{20!}{11! .9!} \\ \\ \\ C_{11}^{20} = -\dfrac{20 . 19.18.17.16. 15. 14. 13. 12. \not 11!}{\not 11! .9!} \\ \\ \\ C_{11}^{20} = -\dfrac{20 . 19.18.17.16. 15. 14. 13. 12.}{9!} \\ \\ \\ C_{11}^{20} = -\dfrac{60949324800
}{362880} \\ \\ \\ =\ \textgreater \ C_{11}^{20} = - 167960 x^{11}$

Answer 2

(a+b)^n

T = Cn,k * (a)^(n-k) * (b)^k

k+1

11ª termo no desenvolvimento de (x-1)^20

T = C20,10 * (x)²⁰⁻¹⁰ * (-1)¹⁰

¹⁰⁺¹

T =20!/[(20-10!)10!] * (x)¹⁰ 

¹⁰⁺¹

T =184756 * x¹º

¹⁰⁺¹