Ratio Test Calculator
What is the Ratio Test?
The ratio test is a method in mathematical analysis used to determine the convergence or divergence of an infinite series. The test evaluates the limit of the absolute value of the ratio of consecutive terms in a series:
Formula: lim (|an+1 / an|), n → ∞
– If the result is less than 1, the series converges.
– If the result is greater than 1, the series diverges.
– If the result equals 1, the test is inconclusive.
Steps to Use the Ratio Test Calculator
Provide the Series Formula:
In the input box provided, enter the formula for the nth term of the series you wish to analyze. For example, these can include formulas like 1/n or n/(n+1).
Submit the Input:
Click the calculate button to initiate the process. The tool will evaluate the series’ ratio and determine its convergence status.
Review the Results:
The result displayed will include:
– The input series formula.
– The calculated ratio limit.
– A clear interpretation of whether the series converges, diverges, or requires further tests for a conclusive answer.
This tool is designed to simplify series analysis for students, mathematicians, or anyone needing to determine convergence efficiently.