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I need to show whether the following serie converges or diverges:

$$\sum_{n=0}^{\infty} (-1)^n \frac{\sqrt{n}}{n+100}$$

I need to use ONLY Leibniz's rule. I started by writing:

$$\sum_{n=0}^{\infty} (-1)^{n-1}(- \frac{\sqrt{n}}{n+100})$$

Now I wanted to show that $- \dfrac{\sqrt{n}}{n+100}$ decreases but I am having trouble showing that.

Can someone help me please.

Thank you in advance

2 Answers 2