Write a MATLAB program in a script file that finds a positive integer n such that the sum of all the integers 1+2+3+cdots+n is a number between 100 and 1000 whose three digits are identical. As output, the program displays the integer
n and the corresponding sum.

Question

Write a MATLAB program in a script file that finds a positive integer n such that the sum of all the integers 1+2+3+cdots+n ﻿is a number between 100 ﻿and 1000 ﻿whose three digits are identical. As output, the program displays the integer 
n ﻿and the corresponding sum.

Accepted Answer

```matlab % Initialize the sum and n sum_of_integers = 0; n = 0; % Loop until the sum is within the specified range and has three identical digits while true % Increment n n = n + 1; % Update the sum of integers from 1 to n sum_of_integers = sum_of_integers + n; % Check if the sum is within the range [100, 1000] if sum_of_integers >= 100 && sum_of_integers < 1000 % Convert the sum to a string to check the digits sum_str = num2str(sum_of_integers); % Check if all three digits are identical if sum_str(1) == sum_str(2) && sum_str(2) == sum_str(3) % Display n and the corresponding sum disp(['n: ', num2str(n)]); disp(['Sum: ', sum_str]); break; % Exit the loop since the condition is met end elseif sum_of_integers >= 1000 % If the sum exceeds 1000, no such n exists disp('No such n exists within the range.'); break; % Exit the loop end end ``` ∻Explanation∻ ⚹The MATLAB script initializes the sum and the integer n. It then enters a loop where it increments n and updates the sum of integers from 1 to n. The loop continues until the sum is within the specified range and has three identical digits. If the sum exceeds 1000, it displays a message that no such n exists within the range.⚹ ∻Step-by-step Instruction∻ ‖ ▪ ⋮ Initialize variables for the sum and n. ‖ ‖ ▪ ⋮ Start a loop that will run indefinitely until the condition is met or exceeded. ‖ ‖ ▪ ⋮ Increment n by 1 in each iteration of the loop. ‖ ‖ ▪ ⋮ Update the sum by adding the new value of n. ‖ ‖ ▪ ⋮ Check if the sum is within the specified range [100, 1000]. ‖ ‖ ▪ ⋮ Convert the sum to a string to check if all digits are identical. ‖ ‖ ▪ ⋮ If the digits are identical, display n and the sum and break the loop. ‖ ‖ ▪ ⋮ If the sum exceeds 1000, display a message that no such n exists and break the loop. ‖ ∻Time Complexity∻ ⚹The time complexity is O(n) because the loop runs until n is found or the sum exceeds 1000. The number of iterations depends on the value of n that satisfies the condition.⚹ ∻Space Complexity∻ ⚹The space complexity is O(1) as the script uses a fixed amount of space for the variables sum_of_integers, n, and sum_str regardless of the input size.⚹

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