How to determine the sum of a infinite geometric series

The video tutorial discusses the concept of infinite series, contrasting it with finite series. It explains how to represent infinite series using Sigma notation and introduces a formula for finding their sum. The tutorial includes a detailed example problem, demonstrating the calculation of an infinite series sum and explaining the concept of convergence, where the series approaches a specific value.

Describe the process the teacher uses to evaluate the infinite series in the example given.

What does the teacher mean by saying that the sum approaches 2/3?