Episode 9 — Patterns and Sequences

Sum of an Infinite Series

Learners will be able to:

• Identify the sum of an infinite geometric series as S∞ = a + ar + ar² + ... • Determine whether a geometric series converges or diverges by examining the value of r. • Apply the test for convergence: if |r| < 1, then the infinite geometric series converges; otherwise it diverges. • Calculate the sum to infinity of an infinite geometric series using the formula S∞ = a / (1 - r), given that |r| < 1. • Solve problems involving the application of the sum to infinity of an infinite geometric series.