MHB Does the Series Converge or Diverge?

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    Convergent Series
shamieh
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determine if series is absolutely convergent, conditionally convergent, or divergent

$$\sum^{\infty}_{n = 1} (n^2 + 9)(-2)^{1-n} $$

which i turned into $$\sum^{\infty}_{n = 1} (n^2 + 9)(-2)^{-n+1} $$

so using the ratio test I got:

$$\frac{((n+1)^2 + 9)(-2)^{-n})}{n^2 + 9 * (-2)^{1-n}}$$

which ended up as n--> infinity becoming $$\frac{2}{3}$$ therefore by ratio test L < 1 so the series converges
 
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nvm I got 1/2
 
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