### Home > CALC > Chapter 2 > Lesson 2.1.1 > Problem 2-11

2-11.

Expand and evaluate each of the following sums. Homework Help ✎

(-4)² + (-3)² + (-2)² + (-1)² + (0)² + (1)² + (2)² + (3)² + (4)² = ___

or, because of the symmetry of *n*^{2}, this problem can be simplified as:

Think about the symmetry of odd functions such as *k*³.

Justify why the sum from −4 to +4 will be 0.

Unfortunately, 2* ^{j}* does not have symmetry across the

*y*-axis. We have to expand and evaluate all terms.

= 2

^{−3}+ 2

^{−2}+ ... + 2

^{2}+ 2

^{1}= _______

sin *x* is an odd function. Consider symmetry before evaluating.