Just came across this problem in one of my past papers (which annoyingly dont come with answers) :

Find as a function of x the sum of the series

x + 3x^2 + 9x^3 + 27x^4 + ((-1)^n)*3^n*x^(n+1) + ....

I have solved similar problems before with binomial and geometric series expressions but I'm not sure how I'd go about this particular series.

Any help?