Is there any general expression for the sum to nth term of the series 1/k? I know that for sufficiently large indices, a good approximation can be ln(b/a) where b and a are the upper and lower limits respectively. I've tried to do something very simple for the exact sum by constructing unit length rectangles between the curve of the function 1/x and the x axis. This shows clearly that as the values of x gets larger and larger, the integral, being the portion of the rectangle below the curve, gets closer and closer to the actual sum, the total area of the rectangles. But I don't seem to be able to get any further than this. I did try to account for the extra (above-curve) portions of the rectangles by treating them approximately as triangles(what better option did I have?) and using the 0.5*b*h formula for their area but later realizing that the heights are changing, I thought it wouldn't be so easy. So, anyone willing to give it a try?