Question

O Coeficiente do termo do binomio de newton (x+1)¹0 que contém x5 é:

a) 45
b) 02
c) 0
d) 16
e) 252

Answer 1

Será o 6° termo:

T (p+1)= C(n, p).

T(5+1) = C(10, 5)

t(6)= 10.9.8.7.6/5! = 252 ✓

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{(x + 1)^{10}}$

$\mathsf{T_{p + 1} = \binom{n}{p}\:.\:A^{n - p}\:.\:B^p}$

$\mathsf{T_{p + 1} = \binom{10}{p}\:.\:x^{10 - p}\:.\:(1)^p}$

$\mathsf{T_{p + 1} = \binom{10}{p}\:.\:x^{10 - p}}$

$\mathsf{10 - p = 5}$

$\mathsf{p = 10 - 5}$

$\mathsf{p = 5}$

$\mathsf{T_{6} = \binom{10}{5}\:.\:x^{5}}$

$\mathsf{T_{6} = \dfrac{10!}{5!.(10 - 5)!}\:.\:x^{5}}$

$\mathsf{T_{6} = \dfrac{10.9.8.7.6.\not5!}{5!.\not5!}\:.\:x^{5}}$

$\boxed{\boxed{\mathsf{T_{6} = 252x^{5}}}}\leftarrow\textsf{letra E}$