Double Sum Computation Issue

Question

I'm trying to compute a double sum...

For scalars, it seems to be working fine. Here is an example:

Sum[ρ^(h - 1)/
 Sum[ρ^x, {x, 0, h - 1}], {h, 1, ∞}] /. {λ -> 
 0.5, μ -> 2.0, ρ -> 0.5}

But for matrices, similar code does not work.

Subscript[I, 2] = IdentityMatrix[2];
e = ({{1, 1}})
p = ({{1, 0}})
B = ( {{μ, -μ}, {0, μ}} )
Q = Transpose[e].p
V = Inverse[B];
EX = p.V.Transpose[e] /. {μ -> 2.0}
A = Subscript[I, 2] + 1/λ B - Q
U = Inverse[A]

Sum[p.MatrixPower[U, h - 1].Transpose[e]/
Sum[p.MatrixPower[U, x].Transpose[e], {x, 0, h - 1}], {h, 
 1, ∞}] /. {λ -> 0.5, μ -> 2.0, ρ -> 0.5}

I am unclear what I am doing wrong. Any help would be appreciated.

Thanks

Lotus · Answer

Continuation of my comment: I meant have:

λ = 0.5; μ = 2.0; ρ = 0.5;

The sum value evaluates to

Also please use i instead of I

=========

Here is the full code:

λ = 0.5; μ = 2.0; ρ = 0.5;

Subscript[i, 2] = IdentityMatrix[2];
e = ({{1, 1}});
p = ({{1, 0}});
B = ({{μ, -μ}, {0, μ}});
Q = Transpose[e].p;
V = Inverse[B];
EX = p.V.Transpose[e] /. {μ -> 2.0};
A = Subscript[i, 2] + 1/λ B - Q;
U = Inverse[A];

N@Sum[p.MatrixPower[U, h - 1].Transpose[e]/
   Sum[p.MatrixPower[U, x].Transpose[e], {x, 0, h - 1}], {h, 
   1, ∞}]

Double Sum Computation Issue

One Answer

Here is the full code:

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