Biggest sum of series in Matlab

Hello.I have a problem to solve in matlab and i don't know how to take it.I ve just started to learn matlab, so i don't know the codes very good.Could you help me with this problem?

EXERCISE:Which is the biggest value of ,,n'' with the property that S(n)=(sum of (k^2) from k=1 to n)<L , where L is given?Solve it using summing and using the formula wich gives us S(n).

Can you help me please to solve this in matlab? I tried to write that sum using the formula:

syms k n

F1 = symsum(k^2,k,1,n).

I don't know how to continue.

Answer 1

[Esen Ozbay]

For this question, I think you should use a for loop and check each number one by one. If you use 'n' in your expression, the result is in terms of 'n'. If you use a number instead of 'n', it will give you the result.

Note: using 'syms' and 'symsum' is not the best way to do this, but I wanted to help you with a code that included the one you already wrote.

Try this:

L = 50; % define L, I chose 50 randomly.

syms k
largest_n = 0; % the largest one we know so far is 0.

for n = 1:sqrt(L)
    % we are trying numbers one by one (going from 1 to sqrt(L)), 
    % I am going only up to sqrt(L) because values greater than this 
    % cannot satisfy our condition by definition. You can start from
    % L as well, but it will slow down your code since it is performing
    % extra calculations for nothing.
    
    F1 = symsum(k^2, k, 1, n);  % F1 is a number, but the variable type is 'symbol'
    F1 = double(F1);    % change the type of F1 to 'double' so that we can do comparisons.
    
    if F1 < L % if the calculated number is smaller than the desired number
        largest_n = n; 
        % the largest n satisfying our condition that we know of is n.
        % if we find a larger n later in the loop, we will change this.
    end
end