match the following series with the series below in which you can compare using the limit comparison test…

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. $sum_{n = 1}^{infty}\frac{1}{n}$, b. $sum_{n = 1}^{infty}\frac{1}{n^{2}}$, c. $sum_{n = 1}^{infty}\frac{1}{n^{3}}$, and d. $sum_{n = 1}^{infty}\frac{1}{n^{3/2}}$ 1. $sum_{n = 1}^{infty}\frac{1}{sqrt{n^{3}+1}}$ does this series converge or diverge? converges 2. $sum_{n = 3}^{infty}\frac{n + 2}{(n + 1)^{3}}$ does this series converge or diverge? converges 3. $sum_{n = 2}^{infty}\frac{1}{2 + n^{3/2}}$ does this series converge or diverge? diverges 4. $sum_{n = 1}^{infty}\frac{n^{2}-1}{n^{5}+2n^{2}+1}$ does this series converge or diverge? converges

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. $sum_{n = 1}^{infty}\frac{1}{n}$, b. $sum_{n = 1}^{infty}\frac{1}{n^{2}}$, c. $sum_{n = 1}^{infty}\frac{1}{n^{3}}$, and d. $sum_{n = 1}^{infty}\frac{1}{n^{3/2}}$ 1. $sum_{n = 1}^{infty}\frac{1}{sqrt{n^{3}+1}}$ does this series converge or diverge? converges 2. $sum_{n = 3}^{infty}\frac{n + 2}{(n + 1)^{3}}$ does this series converge or diverge? converges 3. $sum_{n = 2}^{infty}\frac{1}{2 + n^{3/2}}$ does this series converge or diverge? diverges 4. $sum_{n = 1}^{infty}\frac{n^{2}-1}{n^{5}+2n^{2}+1}$ does this series converge or diverge? converges

Answer

Answer:

(1) D. (\sum_{n = 1}^{\infty}\frac{1}{n^{3/2}}), Converges (2) C. (\sum_{n = 1}^{\infty}\frac{1}{n^{3}}), Converges (3) D. (\sum_{n = 1}^{\infty}\frac{1}{n^{3/2}}), Diverges (4) C. (\sum_{n = 1}^{\infty}\frac{1}{n^{3}}), Converges