10.6.2 converge or diverge? alternating series

[karush]

converge or diverge
$$S_n= \sum_{n=1}^{\infty} (-1)^{n+1}\frac{\sqrt{n}+6}{n+4}$$
ok by graph the first 10 terms it looks alterations are converging to 0

 

[skeeter]

alternating series whose nth term $\rightarrow 0 \implies$ convergence