Because power series resemble polynomials, they’re simple to integrate using a simple three-step process that uses the Sum Rule, Constant Multiple Rule, and Power Rule.For example, take a look at the following integral:[img width=104,height=49]https://www.dummies.com/wp-content/uploads/312161.image0.png[/img][br][br][br]At first glance, this integral of a series may look scary. But to give it a chance to show its softer side, you can expand the series out as follows:[br][br][br][img width=235,height=40]https://www.dummies.com/wp-content/uploads/312162.image1.png[/img][br][br][br]Now you can apply the three steps for integrating polynomials to evaluate this integral:[list=1][*]Use the Sum Rule to integrate the series term by term:[img width=291,height=37]https://www.dummies.com/wp-content/uploads/312163.image2.png[/img][/*][*]Use the Constant Multiple Rule to move each coefficient outside its respective integral:[img width=292,height=37]https://www.dummies.com/wp-content/uploads/312164.image3.png[/img][/*][*]Use the Power Rule to evaluate each integral:[img width=227,height=37]https://www.dummies.com/wp-content/uploads/312165.image4.png[/img][/*][/list]Notice that this result is another power series, which you can turn back into sigma notation:[img width=141,height=53]https://www.dummies.com/wp-content/uploads/312166.image5.png[/img][br][br]