SUMMARY
The discussion focuses on finding the interval of convergence for the power series defined by the sum from n=1 to infinity of (x-11)^n / (n(-9)^n). The user applied the ratio test, arriving at the interval 2 < x < 20, which was confirmed as correct after checking the endpoints. The endpoints were verified, with x = 2 not converging and x = 20 converging, leading to the final conclusion that the interval of convergence is (2, 20].
PREREQUISITES
- Understanding of power series and convergence
- Familiarity with the ratio test for series convergence
- Knowledge of endpoint convergence in power series
- Basic algebra for simplifying inequalities
NEXT STEPS
- Review the ratio test for power series convergence
- Study endpoint convergence in power series
- Explore examples of power series with varying convergence intervals
- Learn about other convergence tests, such as the root test
USEFUL FOR
Students studying calculus, particularly those focusing on series and sequences, as well as educators teaching convergence concepts in power series.