1. ## Determinant

$n\geq 1$Determinant nxn:

$\\D_{n}=\begin{vmatrix} 3 & 2 & 0 & .... & ... & 0 & 0 \\ 1 & 3 & 2 & 0 & ... & 0 & 0 \\ 0 & 1 & 3 & 2 & ... & 0 & 0 \\ . & . & . & . & . & . & .\\ . & . & . & . & . & . & 0\\ 0 & 0 & . & . & 1 & 3 & 2\\ 0 & 0 & . & . & 0 & 1 & 3 \notag \end{vmatrix}$

Prove that for all n $n\geq 1$ - $D_{n}=2^{n+1}-1$

Thank You!

2. ## Re: Determinant

First, what is "n", the number of rows and columns?

Second, what have you tried yourself? Have you calculated $D_n$ for n= 1, 2, or 3? It looks to me as if expanding by "minors" along the first row or first column should give you hints about a proof by induction.