SUMMARY
The discussion centers on determining the convergence or divergence of the infinite series $$\sum_{k = 1}^{\infty} {(\frac{e }{3})}^{k}$$. The series is identified as a geometric series with a common ratio of $$\frac{e}{3}$$. Since the absolute value of the common ratio is less than 1, the series converges. The geometric series test is the appropriate method for this analysis.
PREREQUISITES
- Understanding of geometric series
- Knowledge of convergence tests in calculus
- Familiarity with the properties of limits
- Basic knowledge of the number 'e' and its significance in mathematics
NEXT STEPS
- Study the geometric series convergence criteria
- Learn about other convergence tests such as the Ratio Test and Root Test
- Explore the concept of series and sequences in calculus
- Investigate the properties of the mathematical constant 'e'
USEFUL FOR
Students of calculus, mathematicians, and anyone interested in series convergence analysis will benefit from this discussion.