Part 5/6:
This solidifies the understanding that alternating sequences can still converge, depending on the rate of decay of their terms.
Graphical Interpretation of Limits and Convergence
Visualizing these sequences on a graph can bolster our understanding. For instance, plotting ( a_n ) versus ( n ) for ( a_n = \frac{(-1)^n}{n} ) reveals the alternating nature of the terms, oscillating closer to the x-axis (approaching zero) as ( n ) increases. This serves as a practical examination of limits, facilitating intuitive grasping of otherwise abstract concepts.