This is a really confusing question that I haven't been able to solve:

Normally when I post questions, I write down the working that i've done so far (I hate the people who post on here purely for answers and never intend to solve the questions themselves!) but I really have no idea how to start this.Express the power series:

$\displaystyle 1+\frac{x^3}{3!}+\frac{x^6}{6!}+\frac {x^9}{9!}+......$

in closed form.

(Hint: Use the fact $\displaystyle 1+\zeta+\zeta^2=0$ for the cube root of unity $\displaystyle \zeta=exp(\frac{2\pi i}{3}.))$

Since it wants me to use [tex]z^3=1[tex] this will only give me the first three terms. However, since there's an n number of terms would I need the $\displaystyle z^n=1$?