Chapter 6.2, Problem 79E

In the following exercises, express the sum of each power series in terms of geometric series, and then express the sum as a rational function.

79. $x+x^2-x^3+x^4+x^5+x^6+\mathrm{...}$ (Hint: Group powers $x^{3k},x^{3k-1},$ and $x^{3k-2}$ .)