(Step-by-Step) Show that (cn , r)=(n-r+1)/(r) •(cn , r-1), n(cn-1 , r)=(r+1)(cn , r+1); What is the coefficient of x^3 in (6 x+5)^7 when
Question: Show that
- \(\left(\begin{array}{c}n \\ r\end{array}\right)=\frac{n-r+1}{r} \cdot\left(\begin{array}{c}n \\ r-1\end{array}\right)\),
- \(n\left(\begin{array}{c}n-1 \\ r\end{array}\right)=(r+1)\left(\begin{array}{c}n \\ r+1\end{array}\right)\);
- What is the coefficient of \(x^{3}\) in \((6 x+5)^{7}\) when expanded?
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