$x(t)=$dots$+C_{-2}{e}^{j((-2)*\frac{2}{T})t}+C_{-1}{e}^{j((-1)*\frac{2}{T})t}+C_0{e}^{j((0)*\frac{2}{T})t}+C_1{e}^{j((1)*\frac{2}{T})t}+C_2{e}^{j((2)*\frac{2}{T})t}+$cdots

Task $2$:

a$.$ Rewrite $x(t)$ above but show $3$ more terms on the left and $3$ more terms on the right $($keep the ellipses to indicate the sum is infinite$).$ You may copy, paste and edit the subscripts to save time.

b$.$ Rewrite $x(t)$ in $($a$)$ above for the following case: $x(t)$ can be represented accurately by a truncated series $($the summation limits $n=-N$ to $N$ instead of $-$ to $.$ Let $N=5,$ the period $T=2$ and $C_0=0$ and $C_n=\frac{1}{n^2}$ for nonzeron.

c$.$ Create a table with two columns one for $t$ and one for $x(t).$ Choose values of $t$ from $-2$ to $2$ in steps of $0\mathrm{.}5.$ For each value of $t,$ evaluate the expression in part $b($you can use Matlab or Excel to save time$)$