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This problem first appeared on another thread under Statistics and probability. I found it when I got the same problem, which is as follows
Consider matrices in the form (k+1 k1)
(k1 k+1)
We will call this matrix Mk, find a general expression for Mk to the nth power in terms of k and n.
I tried several different matrices of this form, the general expression i came up with is attached in the thumbnail, but I still tried making it somewhat clear with latex.
M[tex]^{N}_{K}[/tex] = 2[tex]^{n1}[/tex][tex]\left( [(k+1) +(k  1)\sum^{n}_{x=1} k^{x}] [(k1) +(k  1)\sum^{n}_{x=1} k^{x}] \right)[/tex]
[tex]\left([(k  1) +(k  1)\sum^{n}_{x=1} k^{x}] [(k + 1) +(k  1)\sum^{n}_{x=1} k^{x}] \right)[/tex]
Consider matrices in the form (k+1 k1)
(k1 k+1)
We will call this matrix Mk, find a general expression for Mk to the nth power in terms of k and n.
I tried several different matrices of this form, the general expression i came up with is attached in the thumbnail, but I still tried making it somewhat clear with latex.
M[tex]^{N}_{K}[/tex] = 2[tex]^{n1}[/tex][tex]\left( [(k+1) +(k  1)\sum^{n}_{x=1} k^{x}] [(k1) +(k  1)\sum^{n}_{x=1} k^{x}] \right)[/tex]
[tex]\left([(k  1) +(k  1)\sum^{n}_{x=1} k^{x}] [(k + 1) +(k  1)\sum^{n}_{x=1} k^{x}] \right)[/tex]
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