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

or, because of the symmetry of $n^2$, this problem can be simplified as:$=2\sum_{-4}^{0}n^{2}=2\left ( (-4)^{2}+(-3)^{2} +(-2)^{2}+(-1)^{2}\right )=2(30)=60$

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.