I have been stuck, trying to find out how to solve the summation from n=1 to ∞ where $a_n = \frac{(-3)^{n-1} }{ 4^n}$. I think it converges, however I can't figure out exactly how to prove it does. Right now I have as the $\lim_{n \to \infty}$ causes it to be 0, which would make it convergent, but I am not sure if that is right (it being $0$). Also, I am having trouble finding the sum, since there does not seem to be a common ratio.
2026-03-29 19:27:40.1774812460
Figure out if a geometric series converges, and if it does find the sum?
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hint: $\dfrac{(-3)^{n-1}}{4^n} = \dfrac{1}{4}\cdot \left(-\dfrac{3}{4}\right)^{n-1}$