Question

Qual é o 6o termo do desenvolvimento do binômio de Newton (a – 1)⁶? *.

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Termo\,geral\,do\,bin\hat omio\,de\,Newton}\\\sf Dado\,o\,bin\hat omio\,(a+b)^n\,o\,termo\,geral\\\sf \acute e\,dado\,por\\\displaystyle\sf T_{p+1}=\binom{n}{p}\cdot a^{n-p}\cdot b^p \end{array}}$

$\Large\boxed{\begin{array}{l}\sf(a-1)^6\\\sf a=a\,b=-1\\\sf n=6\\\sf p+1=6\\\sf p=6-1\\\sf p=5\\\displaystyle\sf T_{5+1}=\binom{6}{5}\cdot a^{6-5}\cdot (-1)^5\\\sf T_6=\dfrac{6\cdot\diagup\!\!\!5\cdot\diagup\!\!\!4\cdot\diagup\!\!\!3\cdot\diagup\!\!\!2}{\diagup\!\!\!5\cdot\diagup\!\!\!\!4\cdot\diagup\!\!\!3\cdot\diagup\!\!\!2\cdot1} \cdot a^5\cdot(-1)\\\sf T_6=-6a\end{array}}$