Prove that $~f(z)=(z+1)^n~$ will be differentiable.

Question

I was messing around with the Cauchy-Riemann equations and noticed, that for all different $$f(z)=(z+1)^n~,$$ where $~n~$ can be any positive integer.

I've tried the Cauchy-Riemann equations were satisfied. Therefore, it got me wondering how could something like this be proven that for any n the equations will be satisfied?