Converting Series for Comparison Test

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uzman1243

I'm trying to find if this series converges or diverges using the comparison test:

and the answer goes:

My problem is, I am not sure how to go from 1/2^(n+1) to 1/2(1/2)^n.

can you please explain that to me

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Matterwave

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$$\frac{1}{2^{n+1}}=\frac{1}{2\cdot 2^n}=\frac{1}{2}\frac{1}{2^n}=\frac{1}{2}\left(\frac{1}{2}\right)^n$$

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