Find the value of an infinite geometric series

What you'll learn

• Identify the common ratio (r) of an infinite geometric series from a given sequence or summation notation with at least 80% accuracy.
• Determine whether an infinite geometric series converges or diverges based on the absolute value of the common ratio (|r|), justifying the conclusion with a clear explanation of the convergence/divergence criterion in at least 4 out of 5 attempts.
• Calculate the sum of a convergent infinite geometric series using the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio, solving at least 3 out of 4 problems correctly.
• Apply the concept of infinite geometric series to solve real-world problems, such as calculating the total distance traveled by a bouncing ball or determining the long-term value of an annuity, with at least 75% accuracy.