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

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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
  1 Comment
Torsten
Torsten on 3 Apr 2024
What do you mean by "solve the following equations" ? Do you mean "compute T(N) from the alpha-vector" ?

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Answers (2)

Hassaan
Hassaan on 3 Apr 2024
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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It's important to note that the advice and code are based on limited information and meant for educational purposes. Users should verify and adapt the code to their specific needs, ensuring compatibility and adherence to ethical standards.
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Torsten
Torsten on 3 Apr 2024
Edited: Torsten on 3 Apr 2024
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

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