Let the sum to n terms be called S(n)
S(1) = 1/1 = 1 this is the only integer
S(2) = 3/2 not an integer
S(3) = 1/1+1/2+1/3 = 11/6 not an integer
S(4) = 1/1+1/2+1/3+1/4 = 25/12 not an integer
Similarly S(5) = 137/60, S(6) = 49/20, S(7) = 363/140
Generally speaking, adding the next fraction makes the result more complicated.
This is not a formal proof of course, but it seems that they are all fractions.
By the way
S(14) = 1171733/360360
So possibly KatieDidIt! was pulling your leg
Hope this will do,
Regards - Ian
