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2-11.
  1. 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 n2, this problem can be simplified as:

Think about the symmetry of odd functions such as k³.
Justify why the sum from −4 to +4 will be 0.

Unfortunately, 2j does not have symmetry across the y-axis. We have to expand and evaluate all terms.
= 2 −3 + 2 −2 + ... + 22 + 21 = _______

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