Determine whether the infinite geometric series converges or diverges.

Your image is very very small and I can barely read it. But here's what I think it says. Please reply with any necessary corrections.

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.

\(\displaystyle \displaystyle \sum_{k=1}^{\infty} \: 4 \left( \dfrac{1}{3} \right)^{k-1}\)

Regardless, what are your thoughts? What have you tried? For instance, you began by noting that you can move the constant 4 outside the sum, and then you noted it's a geometric series, allowing you to automatically know... what?
 
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