# Calculating Coefficients for a Power Series

Keywords: Small Group Activity, Taylor and Power Series

### Highlights of the activity

1. This small group activity is designed to help students practice finding power series coefficients.
2. Students are asked to find the power series coefficients for $\sin(\theta)$ using the general formula for power series coefficients.
3. The wrap-up discussion focuses on what these coefficients tell you, where this approximation valid, and how you would ‘shift’ your power series approximation point.

### Reasons to spend class time on the activity

Power series are an important middle division topic, leading to ideas about making approximations and solving differential equations. Students often have trouble at this stage wrangling with series notation and the multiple representations of a function (functional form, power series expansion, graph). This activity allows students to practice generating a power series expansion for a function.

### Student Handouts

Authors: Corinne Manogue

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