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Consider the series:

$$\sum_{n=1}^{\infty }\frac{n^{2}}{2^{n}}$$

If the ratio test is applied in the series, which of the following inequalities results, showing that the series converges?

A

$$\lim_{n\rightarrow \infty }\cfrac{n^{2}}{2^{n}}<1$$

B

$$\lim_{n\rightarrow \infty }\cfrac{2^{n}}{n^{2}}<1$$

C

$$\lim_{n\rightarrow \infty }\cfrac{\left (n+1 \right )^{2}}{2n^{2}}<1$$

D

$$\lim_{n\rightarrow \infty }\cfrac{2n^{2}}{\left (n+1 \right )^{2}}<1$$

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