Hi guys, I think this is easy, but I keep getting stuck!

"Prove the series $\displaystyle \sum_{n=1}^{\infty} (1+n)^{-z}$ converges for all complex z with real part strictly greater than 1."

I assume we take the absolute value $\displaystyle \sum_{n=1}^{\infty} |(1+n)^{-z}|$

and then $\displaystyle \sum_{n=1}^{\infty} |(1+n)^{-Re(z)}||(1+n)^{-Im(z)}|$

$\displaystyle \leq \sum_{n=1}^{\infty} |(1+n)^{-Re(z)}|$

But where to now, I assume the comparison test, but what would one compare this too?

Many thanks,

Yaad