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I am trying to find a theorems or convergence tests that can help me formally prove that this sequence converges to 0:

$$\{(3+n^2)(1/2)^n\}_{n\epsilon\Bbb{N}}$$

I am very new to convergence and divergence proofs, so I'm not quite sure where to start. Any pointers would be greatly appreciated!

Gustav
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    Informally, polynomials grow (much) slower than exponentials. In this case $\frac{n^2}{2^n}\to 0$ is sufficient. – AlvinL Aug 31 '23 at 13:14
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    Hard to know what theorems or tests to reference w/o knowing first which ones you've seen or have access to – Benjamin Dickman Aug 31 '23 at 13:30
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    Apply the ratio test: if $|a_{n+1}|/|a_n|\to a<1$ then $a_n\to 0.$ In your case $|a_{n+1}|/|a_n|\to {1/2}.$ Actually the ratio test implies that the series $\sum a_n$ is absolutely convergent, hence $a_n\to 0.$ – Ryszard Szwarc Aug 31 '23 at 13:36

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