Question

considere o desenvolvimento de ( ×+ 1 ) elevado a 15
calcule o coeficiente de × elevado a 13

Answer 1

$(x+1)^{15}= \begin{pmatrix}15\\0\end{pmatrix}\cdot x^{15}+\begin{pmatrix}15\\1\end{pmatrix}\cdot x^{14}+\begin{pmatrix}15\\2\end{pmatrix}\cdot x^{13}+\cdots$

$\begin{pmatrix}15\\2\end{pmatrix}=\dfrac{15!}{2!13!}=\dfrac{15\cdot14}{2\cdot1}=105$