Infinite Series Decision Flowchart

Use this quick guide to help decide whether an infinite series converges. It is designed as a study aid for common Calc II convergence tests and patterns.

Quick reminders

  • If \(\lim_{n \to \infty} a_n \neq 0\), the series diverges immediately.
  • Alternating series may converge conditionally if terms decrease to 0.
  • Geometric series converge when \(|r| < 1\).
  • Factorials and exponentials usually beat polynomials in the long run.