Match the following series with the series below in which you can compare using the Limit Comparison Test. Then determine whether the series converge or diverge.

A. $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n}$,     B. $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^2}$,     C. $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^3}$,    and     D. $\displaystyle \sum_{n=1}^{\infty}\left(\frac{1}{2}\right)^{n-1}$

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1. ? A B C D $\displaystyle \sum_{n=1}^{\infty}\frac{n+3}{n^2}$   Does this series converge or diverge? ? Converges Diverges

2. ? A B C D $\displaystyle \sum_{n=1}^{\infty}\left(\frac{2}{2^{n}+5}\right)$   Does this series converge or diverge? ? Converges Diverges

3. ? A B C D $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^2+4}$   Does this series converge or diverge? ? Converges Diverges

4. ? A B C D $\displaystyle \sum_{n=1}^{\infty}\frac{n-5}{n^4+1}$   Does this series converge or diverge? ? Converges Diverges

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