That series, the harmonic series, diverges. Can't put the symbols to make this simple but the area under the curve of the function 1/x from x=1 to x=infinite, or the integral from x=1 to x = infinite of 1/x dx is less than the sum of the rectangles of height 1/n and width 1 from n=1 to n=infinite. The mentioned integral diverges and therefore so does the series.