MHB 10.6.2 converge or diverge? alternating series

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The series S_n = ∑_{n=1}^{∞} (-1)^{n+1} (√n + 6)/(n + 4) is analyzed for convergence. Graphing the first ten terms suggests that the terms are alternating and approaching zero. According to the alternating series test, if the nth term approaches zero, the series converges. Therefore, the conclusion drawn is that the series converges. This aligns with the principles of alternating series and their behavior in convergence analysis.
karush
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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
 
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alternating series whose nth term $\rightarrow 0 \implies$ convergence
 

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