Question

//calcule o valor de expressão usando a propriedade de triangulo pascal (7/1) + (7/2 + ... + (7/6) + (7/7) =

Answer 1

$\begin{matrix} 1\\ 1&1\\ 1&2&1\\ 1&3&3&1\\ 1&4&6&4&1\\ 1&5&10&10&5&1\\ 1&6&15&20&15&6&1\\ 1&7&21&35&35&21&7&1 \end{matrix}\\ \\ \\ \displaystyle S=\binom{7}{1}+\binom{7}{2}+\binom{7}{3}+\binom{7}{4}+\binom{7}{5}+\binom{7}{6}+\binom{7}{7}\\\\ S=7+21+35+35+21+7+1\\ \\ S=127\\ \\ \texttt{Note: }\sum_{i=0}^{n}\binom{n}{i}=2^n$