Ensino Médio ⇒ Triângulo de Pascal Tópico resolvido

[owen123]

Encontre o valor de:

[tex3]\begin{pmatrix}
10 \\
0 \\
\end{pmatrix}-\begin{pmatrix}
9 \\
0 \\
\end{pmatrix}+\begin{pmatrix}
10 \\
1 \\
\end{pmatrix}-\begin{pmatrix}
9 \\
1 \\
\end{pmatrix}+ ... +\begin{pmatrix}
10 \\
9\\
\end{pmatrix}-\begin{pmatrix}
9 \\
9 \\
\end{pmatrix}+\begin{pmatrix}
10 \\
10\\
\end{pmatrix}[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\begin{pmatrix}
10 \\
0 \\
\end{pmatrix}-\begin{pmatrix}
9 \\
0 \\
\end{pmatrix}+\begin{pmatrix}
10 \\
1 \\
\end{pmatrix}-\begin{pmatrix}
9 \\
1 \\
\end{pmatrix}+ ... +\begin{pmatrix}
10 \\
9\\
\end{pmatrix}-\begin{pmatrix}
9 \\
9 \\
\end{pmatrix}+\begin{pmatrix}
10 \\
10\\
\end{pmatrix}[/tex3]

[csmarcelo]

[tex3]\begin{pmatrix}
10 \\
0 \\
\end{pmatrix}-\begin{pmatrix}
9 \\
0 \\
\end{pmatrix}+\begin{pmatrix}
10 \\
1 \\
\end{pmatrix}-\begin{pmatrix}
9 \\
1 \\
\end{pmatrix}+ ... +\begin{pmatrix}
10 \\
9\\
\end{pmatrix}-\begin{pmatrix}
9 \\
9 \\
\end{pmatrix}+\begin{pmatrix}
10 \\
10\\
\end{pmatrix}=[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\begin{pmatrix}
10 \\
0 \\
\end{pmatrix}-\begin{pmatrix}
9 \\
0 \\
\end{pmatrix}+\begin{pmatrix}
10 \\
1 \\
\end{pmatrix}-\begin{pmatrix}
9 \\
1 \\
\end{pmatrix}+ ... +\begin{pmatrix}
10 \\
9\\
\end{pmatrix}-\begin{pmatrix}
9 \\
9 \\
\end{pmatrix}+\begin{pmatrix}
10 \\
10\\
\end{pmatrix}=[/tex3]

[tex3]=\begin{pmatrix}
10 \\
0 \\
\end{pmatrix}+\begin{pmatrix}
10 \\
1 \\
\end{pmatrix}+ ... +\begin{pmatrix}
10 \\
9\\
\end{pmatrix}+\begin{pmatrix}
10 \\
10\\
\end{pmatrix}-\[\begin{pmatrix}
9 \\
0 \\
\end{pmatrix}+\begin{pmatrix}
9 \\
1 \\
\end{pmatrix}+...+\begin{pmatrix}
9 \\
9 \\
\end{pmatrix}\]=[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]=\begin{pmatrix}
10 \\
0 \\
\end{pmatrix}+\begin{pmatrix}
10 \\
1 \\
\end{pmatrix}+ ... +\begin{pmatrix}
10 \\
9\\
\end{pmatrix}+\begin{pmatrix}
10 \\
10\\
\end{pmatrix}-\[\begin{pmatrix}
9 \\
0 \\
\end{pmatrix}+\begin{pmatrix}
9 \\
1 \\
\end{pmatrix}+...+\begin{pmatrix}
9 \\
9 \\
\end{pmatrix}\]=[/tex3]

[tex3]=2^{10}-2^9=2^9[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]=2^{10}-2^9=2^9[/tex3]