Part 5/5:
L = \frac{-1 + \sqrt{5}}{2} \approx 0.618033...
]
This result demonstrates that the sequence not only converges but does so to a well-defined limit, illustrating the interplay between algebra and calculus in exploring the behaviors of sequences.
Conclusion
Through the exploration of sequence limits and the convergence properties established, we can efficiently determine the limits of defined sequences. This exercise in calculus illustrates both theoretical and practical applications in determining the behavior and end values of sequences as they progress indefinitely. The findings stress the significance of understanding foundational mathematical principles necessary for navigating more complex analyses in calculus and beyond.