So, I was reading about the integral test for convergence of a series from wikipedia, which says that the series converges if the integral of the monotonically decreasing function converges, but to my intuition
Simply because the function is monotonically decreasing and positive. In that case I might have integrals converging and the series diverging, all I would be able to say is that if the integral diverges, the series definitely diverges. I mean, it looks like a test of divergence more than a test of convergence. Am I going wrong somewhere? Any help is sincerely appreciated since I am not one with a formal mathematical background.