Mathematical analysis

Sequences and Series

Find out whether a sequence or series converges and why. Each supported result includes the chosen method, the assumptions to check, and the mathematical steps.

Sequences Series

General term \(a_n\)

Examples:

More examples

Starting index Terms on graph

Enter the series term: 1/n^2 for a numerical series, x^n/n^2 or (x-2)^n/(n+1)^2 for a power series. The calculator automatically recognizes its center and uses the selected value of x for the graph. Always write multiplication using *.

Enter an expression above and select Analyze to see the result, graph, and explanation.

Method and reliability

The calculator explains which test is used and why. Unsupported expressions are labeled undetermined, without inferring convergence from a graph. Reproducible stress tests are included in tests/ for command-line use, separate from the public website.