Infinite Series Convergence Calculator

🔢 Infinite Series Convergence Calculator

Enter nth term aₙ of the series ✍️ Choose Test Method ⚙️ Ratio Test Root Test Enter n (for approximation) 🔢 🔍 Check Convergence

🧠 What is an Infinite Series Convergence Calculator?

The Infinite Series Convergence Calculator determines whether a given infinite series converges or diverges using common mathematical tests such as the Ratio Test or Root Test.

⚙️ How to Use

1. Enter the nth term expression of the series (like 1/n^2 or (2^n)/(n!)).
2. Select the test method — Ratio or Root test.
3. Provide a value of n for approximation (e.g., 10).
4. Click Check Convergence to see the result instantly.

📘 Understanding Convergence

An infinite series converges if its sum approaches a finite number as n → ∞. Otherwise, it diverges. This tool simplifies determining convergence for various series types.

✨ Benefits of This Tool

• Quickly determines if a series converges or diverges.
• Helps in learning and verifying series behavior.
• Useful for students, educators, and researchers.
• Supports fractional, exponential, and factorial series forms.

🔗 Related Tool

For deeper analysis, check our Radius of Convergence Calculator — it helps determine the radius and interval where a power series converges.

🏁 Conclusion

The Infinite Series Convergence Calculator is a practical and educational tool for understanding the behavior of series. Whether you’re studying calculus or analyzing numerical methods, this calculator offers an intuitive way to test convergence efficiently. 🚀