How can I analyze the sum and product together in a code?

Hello,

I have just started to learn matlab and tried to solve the following equations:

where,

and the values of alpha(j) will be retrieved from an excel file containing 10 values of it.

Can someone let me know the procedure?

Thank you

[Torsten]

What do you mean by "solve the following equations" ? Do you mean "compute T(N) from the alpha-vector" ?

Answer 1

[Hassaan]

An initial Idea:

% Assuming the Excel file is named 'alpha_values.xlsx' and the values are in the first column
alpha = xlsread('alpha_values.xlsx', 'A1:A10'); % Adjust the range based on the actual data location

% Compute the denominator of π(N, O)
product_terms = cumprod(alpha); % Cumulative product of alpha values
denominator = 1 + sum(product_terms);

% Calculate π(N, O)
pi_N_O = 1 / denominator;

% Initialize the sum for T(N)
T_N_sum = 0;

% Calculate the sum for T(N)
for i = 1:length(alpha)
    if i == 1
        product = 1; % The product term for i=1 is 1 since it has no previous alpha values
    else
        product = product_terms(i-1); % Product of all alpha values up to i-1
    end
    T_N_sum = T_N_sum + ((i - 1) * product);
end

% Finally, compute T(N)
T_N = pi_N_O * T_N_sum;

% Display the result
disp(T_N);

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Answer 2

[Torsten]

rng("default")
N = 10;
mu = 1;
alpha = rand(1,N);
alphap = cumprod(alpha);
fak = factorial(0:N);
terms_numerator = alphap./(fak(1:end-1).*mu.^(0:N-1));
terms_denominator = alphap./(fak(2:end).*mu.^(1:N));
format long
T = sum(terms_numerator) / (1 + sum(terms_denominator))

T = 
   0.733481020109729