Summations and Limits to Find Area

The following picture shows the six equations used in this lesson:

Here is an example of a problem that utilizes nearly all of the above equations:

Equation #6 is used throughout the first half of this problem. The main strategy is to factor 1/n out of the equation, then putting it outside of the summation. Once 1/n is removed three times so it's 1/n^3, you have to split up the summation into three summations using rule #5. You then use rule #1, #2, and #3, respectively, to simplify each summation. Simplify, then take the limit.