Question

HELP PLEASE

Answer 1

Does it Diverge or Converge?

\[\sum_{n=1}^{\infty}\frac{ 1 }{ \sqrt{n+7} }\]

Answer 2

Apparently it Diverges....

Answer 3

I tried using the integral test.

\[\int\limits_{1}^{\infty}\frac{ 1 }{ \sqrt{x+7} } \left( u=x+7 ,du=dx \right) \rightarrow \int\limits \frac{ 1 }{ u^{1/2} }\]
\[\left[ 2u^{1/2} \right] \rightarrow \left[ 2(n+7)^{1/2} \right]_{1}^{\infty}\]
\[\left[ 2(\infty+7)^{1/2}- ....\right]\]

Wow okay. I figured out why it diverges... Lol