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

2-11.

Expand and evaluate each of the following sums.

or, because of the symmetry of

, this problem can be simplified as:Think about the symmetry of odd functions such as

.

Justify why the sum fromto will be . Unfortunately,

does not have symmetry across the -axis. We have to expand and evaluate all terms.

_______ is an odd function. Consider symmetry before evaluating.