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

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I have just started to learn matlab and tried to solve the following equations:
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 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 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
product = product_terms(i-1); % Product of all alpha values up to i-1
T_N_sum = T_N_sum + ((i - 1) * product);
% Finally, compute T(N)
T_N = pi_N_O * T_N_sum;
% Display the result
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Torsten on 3 Apr 2024
Edited: Torsten on 3 Apr 2024
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 =


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