Ratio Convergence Chart
Terms Visualization
Calculated Values
| n | an | an+1 | |an+1 / an| | Status |
|---|
The Ratio Test Calculator is a smart tool to find out if an infinite series converges or diverges. It helps students and teachers by quickly applying the ratio test rule without needing manual calculation. Great for math learners, especially in calculus and advanced mathematics.
What Is the Ratio Test?
The ratio test is a method used in calculus to test whether a series converges or not. It compares the absolute value of the ratio between successive terms in a series. If the ratio is less than 1, the series converges. If it’s greater than 1, the series diverges. If the ratio equals 1, the test is inconclusive.
How to Use the Ratio Test Calculator
Steps to use this calculator:
- Enter the formula or terms of the series (like an)
- The calculator will compute the limit of |an+1 / an|
- You’ll get the result with an explanation if the series converges or diverges
Ratio Test Formula
The ratio test uses this limit formula:
lim (n→∞) |an+1 / an| = L
- If L < 1 → the series converges
- If L > 1 → the series diverges
- If L = 1 → the test is inconclusive
Why Use This Calculator?
- It saves time on solving limits manually
- Gives instant results with steps
- Good for exam prep and homework help
- Supports learning through easy explanations
Example
For the series ∑ (n! / nāæ), input the term formula into the calculator. The result will show:
L = 0 → Since L < 1, the series converges.
Conclusion
Understanding infinite series is easier with the Ratio Test Calculator. It’s a simple tool that gives quick answers and helps you learn how the ratio test works. Use it when you're stuck or to double-check your solution during studies.