Sum of a series containing table column data

I have a table, T, with one column of data of length 12054. I need to then make the following sum

SUM_[k=0 to t-1] 0.5^abs(k-5)*T(t-k)

lambda(t) = 1 + ---------------------------------------------------------------

SUM_[k=0 to t-1] 0.5^abs(k-5)

I have tried using symsum and defining the numerator and denominator seperately but I cannot seem to get it right. If anyone could help me with this it would be much appreciated.

Edit: Below is my attempt

syms k x;
% S1(t) is my attempt at defining the numerator
S1(t) = symsum(0.5^(abs(k-5)*T(t-k)),k,0,t-1);
Unrecognized function or variable 't'.

% Next is my attempt at defining the denominator
for t=0:12054
S2(t) = symsum(0.5^(abs(k-5)),k,0,t-1);
end
Array indices must be positive integers or logical values.

Error in sym/privsubsasgn (line 1151)
                L_tilde2 =
                builtin('subsasgn',L_tilde,struct('type','()','subs',{varargin}),R_tilde);

Error in sym/subsasgn (line 972)
            C = privsubsasgn(L,R,inds{:});

            

Edit 2: Second attempt at defining the numerator

syms k x;
>> for t=1:12054
S1(t) = symsum(0.5^(abs(k-5)*T(t-k)),k,0,t-1);
end
Error using sym/subsindex (line 864)
Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments
must be symbolic variables, and function body must be sym expression.            

[Yongjian Feng]

It makes more sense if you post your solution here first, then we can help you to improve it.

[Leo Tu]

Sorry @Yongjian Feng, I have edited the post.

Answer 1

[Leo Tu]

For anyone interested, I have found a solution.

V = flip(T,1) 
syms k; 
for t=1:12054 
L(t) = 1+symsum(.5.^abs(k-5)*V(t),k,0,12054-t)./symsum(.5.^abs(k-5),k,0,12054-t); 
end 
lambda = double(L); 
lambda = flip(lambda,2)  % flipping back because we initially flipped T to get V. 

Answer 2

[Sulaymon Eshkabilov]

What is the value of k? Just presuming k is taken from the number of elements in T, the calc can be done, e.g:

k=0:numel(T)-1;
L=1+sum(.5.^abs(k-5)*T(1:end-k))./sum(.5.^abs(k-5));

[Leo Tu]

Hi there, k is the summation index from k = 0 to k = t-1, where t is in relation to T(t) for t=1:12054.

So the result lambda(t) would be a vector (I think) of length 12054.