Question

O 4° termo no desenvolvimento de (x2 + 1/x)6 é?

Answer 1

Resposta:

T4 = 20x³

Explicação passo-a-passo:

a = x²

b = x⁻¹

n = 6

p = 3

$T_{p+1}=\left \(( {{n} \atop {p}}) \right.a^{n-p}.b^{p}\\\\\\ T_{3+1}=\left \(( {{6} \atop {3}}) \right.(x^{2}) ^{6-3}.(x^{-1} )^{3}\\\\T_{3+1}=\left \(( {{6} \atop {3}}) \right.(x^{2}) ^{3}.(x^{-1} )^{3}\\\\T_{3+1}=\left \(( {{6} \atop {3}}) \right.x^{6} ^{}.x^{} ^{-3}\\\\\\ T_{4}=\left \(( {{6} \atop {3}}) \right.x^{3}\\\\T4 = \frac{6!}{3!.3!}x^{3}\\\\T4 =\frac{6.5.4.3!}{6.3!}x^{3}\\\\T4=20x^{3}$