Series Calculator

Find a local power series expansion for common functions.

Use this calculator as a study checker

Enter the problem carefully, review the interpreted input, and compare each step with your own work. Calculus results can depend on notation, variables, bounds, domains, and assumptions.

Check the method before copying the answer.
Use the examples below to test nearby problems.
Read the calculus guides for worked explanations.

Solution

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Enter an expression or choose an example to calculate.

Series Examples

What this calculator is for

A series adds a sequence of terms, sometimes infinitely many. In calculus, series approximate functions and help analyze convergence. Use it to check your setup, compare steps with your own work, and review the meaning of the final expression before copying it into homework.

How series expansions are built

Identify whether the task asks for a power series, a known standard series, or convergence behavior.
Use known series such as sine, cosine, exponential, and geometric series when possible.
State the center and the interval where the expansion is valid when relevant.

Manual example

Problem: expand \(\sin x\) near \(0\).
The Maclaurin series is \(x-x^3/3!+x^5/5!-\cdots\).
Near zero, using the first few terms gives a practical polynomial approximation.

Common mistakes to avoid

Using a series outside its interval of convergence.
Mixing Taylor coefficients with ordinary polynomial coefficients.
Forgetting alternating signs in sine and cosine expansions.

When to double-check the result

Series pages are intended for learning and approximation. For convergence proofs, compare the generated reasoning with your course method.