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Write a MATLAB program to determine how many terms are required for the sum of the series \( y \) to exceed 20000. What is the sum of this number of terms?

Answer :

Here's an example MATLAB program that calculates the number of terms required for the sum of a series to exceed 20000 and calculates the sum of that number of terms

How to explain the program

% Initialize variables

n = 1; % Number of terms

sumValue = 0; % Sum of the terms

% Calculate the sum of the series until it exceeds 20000

while sumValue <= 20000

% Calculate the nth term of the series

term = 1/n^2;

% Add the nth term to the sum

sumValue = sumValue + term;

% Increment the number of terms

n = n + 1;

end

% Subtract 1 from n because the loop increments n once more after the sum exceeds 20000

n = n - 1;

% Display the number of terms and the sum of that number of terms

disp(['Number of terms required: ', num2str(n)]);

disp(['Sum of ', num2str(n), ' terms: ', num2str(sumValue)]);

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