# Series Derivative

## Prompt

“Write the first 5 terms of y”(x).”

where y”(x) is the second derivative of y(x) expanded as a series solution.

## Context

This SWBQ helps students to see what happens to a power series when derivatives are taken as a lead-in to reindexing a sum.

## Wrap Up

After the terms have been written, discuss how the terms can be reindexed so that the sum has the same powers of xn as other sums in the differential equation.

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