Does $\frac{1}{4}=\sum\_{n=0}^{\infty}(-1)^n3^n$ when expressed as a series?

To see if the series converges to $\frac{1}{4}$, I have to evaluate the series. I feel like this equation is wrong, since this is an alternating series, and using a test we see that $3^n$ is always growing, which means it diverges. That means $\frac{1}{4}$ is impossible to get as a number. Is my conclusion correct?