# Alternating Series Test for Convergence - can the sequence be initially non-decreasing?

I was offered the adhering to question:

Determine if the adhering to collection is convergent. You might make use of standard collection, yet you need to plainly state which results or rules you make use of.

$$\sum_{n=1}^{\infty} \frac{(-1)^{n+1}\sqrt{n}}{n+4}$$

Does the Alternating Series Test call for the favorable term $\frac{\sqrt n}{n+4}$ to be lowering for all $n$ or is it enough that the term is *at some point * lowering? ($\frac{\sqrt n}{n+4}$ is lowering just for $n>3$.)

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Ryan 2022-07-25 20:42:02

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