Need to find the smallest [n] such that the sum for a harmonic series is greater than some value X.

I am new to programming/MATLAB and I know the attached code is incorrect, but I am lost. My goal is to find the smallest n-value such that the sum for a harmonic series is greater than some integer value (say 10). However, when I print [n], I just get the defined n value in the first line of code. I have commented my code to reflect my understanding. Please call me out when needed.

n = 200;                  %max number of rows that will print
S = 0;                  %initial starting value of sum

for i = 1:n              %for the rows 1 to n (i.e. 200 rows)
    S = S + 1/i;         %apply this fn. to each element
                         
    if S >= 10           %if the sum (S) is greater than 10
        break            %the loop "breaks" (i.e. stops applying the fn.)
    end                  %ends the break
end                      %ends the loop from row 1 to 200

n

Answer 1

[Walter Roberson]

n = 25000;                  %max number of rows that will print
S = 0;                  %initial starting value of sum

for i = 1:n              %for the rows 1 to n (i.e. 200 rows)
    S = S + 1/i;         %apply this fn. to each element
                         
    if S >= 10           %if the sum (S) is greater than 10
        break            %the loop "breaks" (i.e. stops applying the fn.)
    end                  %ends the break
end                      %ends the loop from row 1 to 200

i

i = 12367

S

S = 10.0000

[Edna1]

Thank you so much! I was very close then apparently. I tried printing [i] previously, but it looks like when the n-range is not large enough, it just returns the limit of the variable (until guessing the sufficient range limit).

Thanks again!