toplam sembolü

Question

$\sum _{k=1}^{10}\left( \begin{matrix} 10\\ k\end{matrix} \right) .3^{10-k}$  ifadesinin sonucu?

$4^{10}-3^{10}$

Answer 1

$\sum_{k=1}^{10}\left(\begin{matrix} 10\\k \end{matrix}\right).3^{10-k}+\left(\begin{matrix} 10\\0 \end{matrix}\right).3^{10}=(1+3)^{10}$

$\sum_{k=1}^{10}\left(\begin{matrix} 10\\k \end{matrix}\right).3^{10-k}=(1+3)^{10}-\left(\begin{matrix} 10\\0 \end{matrix}\right).3^{10}$

$\sum_{k=1}^{10}\left(\begin{matrix} 10\\k \end{matrix}\right).3^{10-k}=4^{10}-3^{10}$ olur.