This counterexample uses the harmonic series and the comparison test to show that the infinite approaching of the terms of a series toward zero is an insufficient condition toward converging the series. In this particular case, adding an infinitude of \(\frac{1}{2}\) terms certainly will not converge a series. In fact, it will produce a divergent series whose sum is infinity.

Is trajectory the same as destination? Small steps are not always insignificant when viewed within a larger context. How can small steps be grouped in order to produce results? Sometimes the most vital perspective is found by zooming out and remapping the details of a situation.

Is trajectory the same as destination? Small steps are not always insignificant when viewed within a larger context. How can small steps be grouped in order to produce results? Sometimes the most vital perspective is found by zooming out and remapping the details of a situation.