Calculate sum of$ (1-2^n) / 3^n$ I feel incredibly stupid right now, but I am not able to calculate the sum of this infinite series...
$\displaystyle \sum_{n=0}^{+\infty} (1-2^n) / 3^n$
I've gone through the first terms, as all the terms are negative I can't see how it is an telescopic series and I also can't see a common radius for it to be a geometric series!

$$=\sum_{n=0}^\infty\left(\frac13\right)^n-\sum_{n=0}^\infty\left(\frac23\right)^n$$
Now for $|r|<1, \sum_{n=0}^\infty ar^n=\dfrac a{1-r}$
