Question

SOCORROOO. (FGV)- O termo independente de x do desenvolvimento de (x+1/x(elevado a 3) elevado a 12 é:

Answer 1

(x + 1/x³)¹² = ( x + x⁻³)¹²

$T_{p + 1} = \left(\begin{array}{ccc}n\\p\end{array}\right) a^{n-p}*b^{p} \\ \\ T_{p+1}= \left(\begin{array}{ccc}12\\p\end{array}\right) x^{12-p} * (x^{-3} )^p \\ \\ T_{p+1} }= \left(\begin{array}{ccc}12\\p\\\end{array}\right) x^{12-p{} }* x^{-3p} \\ \\ T_{p+1}= \left(\begin{array}{ccc}12\\p\end{array}\right) x^{12-4p} \\ \\ \text{O termo sera independente, quando 12 - 4p=0} \\ \\ -4p=-12=\ \textgreater \ 4p=12=\ \textgreater \ p=3 \\ \\ T_{3+1}= \left(\begin{array}{ccc}12\\3\\\end{array}\right) } x^0$

$T_{4}= \left(\begin{array}{ccc}12\\3\\\end{array}\right).1 \\ \\ T_{4}= \frac{12!}{3!9!} = \frac{12.11.10.9!}{3.2.1.9!}= 2.11.10 = 220$