# Sums and Series for Square and Cube Summations

Lesson Summary

Students learn how to evaluate the sums of squares and cubes using summation formulas. The lesson begins with basic exercises that introduce the concepts and the formulas

$$\sum_{r=1}^{n} r^2 = \frac{1}{6} n(n+1)(2n+1)$$ and

$$\sum_{r=1}^{n} r^3 = \frac{1}{4} n^2 (n+1)^2$$.

This allows students to practice calculating sums with simple ranges, reinforcing their understanding of the formulas.

As the lesson progresses, the problems become more complex, involving scenarios such as evaluating sums over different intervals and finding the sum of squares of odd numbers. Students apply their skills to sum terms from specific starting points and incorporate algebraic manipulations to solve more challenging problems.

##### Tutorials

Sums of Squares and Cubes Part 1

Sums of Squares and Cubes Part 2

Sums of Squares and Cubes Part 3

Sums of Series

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