Radius of Convergence

From the Calculus II: Taylor & Maclaurin Series curriculum · Updated Jan 11, 2026

Ratio Test Application

Not all series converge for all x. To find the Interval of Convergence, we typically use the Ratio Test.

The Logic:

  1. Take the limit as n approaches infinity of |a_(n+1) / a_n|.
  2. Set the result < 1 to find the values of x where it converges.
  3. Check Endpoints: Always plug the endpoints back into the original series to check for conditional convergence.

Homework Help: Use our AI Math Solver to check your ratio test steps if you keep getting 'Infinity'.

Get the full Calculus II: Taylor & Maclaurin Series curriculum

Clone the complete plan to your dashboard for unlimited AI-generated notes, practice quizzes, and a personalised revision schedule.

Create Free Account