An Asymptotic Study on the Ratio of Consecutive Terms in Mixed Exponential-Power Sequences Centered on the Definition of the Natural Constant e

Key Points

• The study aims to explore the behavior of ratios in mixed exponential-power sequences focusing on the natural constant e.
• Conducted an asymptotic analysis of mixed exponential-power sequences.
• Examined the limit behavior of ratios of consecutive terms.
• Applied mathematical definitions related to the natural constant e.
• Identified specific patterns in the ratios of consecutive terms.
• Revealed the significance of the natural constant e in these sequences.
• Provided insights on the long-term behavior of these mathematical sequences.