Prove that the following series is diverges!

Question

$$\sum_{n=0}^\infty \frac{\sqrt n}{n+7}$$

I tried to use the comparison test and I know I should use a lower comparison since it's very much likely diverges but had problems lowering the square root. (According the estimation I did)

Could you help me with the comparison test? (or any other hint if you would use other tests)

EDIT: The exam actually asks if it diverges or convergent but I know it's diverges, just can't prove it yet.

Answer 1

Ignoring the first term and shifting the index,

$$\sum_{n=1}^\infty\frac{\sqrt n}{n+7}=\sum_{n=8}^\infty\frac{\sqrt{n-7}}{n}>\sum_{n=8}^\infty\frac1{n}.$$

Hence the series diverges.