Question

Check the convergence or divergence of the following series

(i) ∑ √𝑛

3 + 1 − √𝑛

3 − 1

∞

𝑛=1

(ii) ∑

7

𝑛+1

9

𝑛

∞

𝑛=1

(iii) ∑

𝑛

3

3

𝑛

∞

𝑛=1

(iv) 1

𝑒

+

4

𝑒

2 +

27

𝑒

3 …