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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Find the sum of the infinite series: 4 + 2 + 1 + ...
💡 Hint: Identify the first term and the ratio, then apply the formula.
Question 2
Easy
What is the common ratio in the series: 3, 1.5, 0.75, ... ?
💡 Hint: Divide one term by the previous one.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What condition must the common ratio meet for an infinite geometric series to converge?
- r > 1
- |r| < 1
- |r| = 1
💡 Hint: Think about how the terms behave when we reach infinity.
Question 2
The sum of an infinite geometric series can be calculated with which formula?
💡 Hint: Remember the components: first term and common ratio.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
You have an infinite geometric series with the first term 8 and a common ratio of 0.3. Find the convergence sum.
💡 Hint: Use the sum formula provided earlier.
Question 2
If you deposit $2000 with an interest rate of 3% compounded annually and let it work for infinitely many years, what would be the total value?
💡 Hint: Remember to account for the terminating behavior of the series.
Challenge and get performance evaluation