This is a question from Jech's Set Theory (Ex. 17.12) which I'm reading at the moment and pretty much stuck on.

If $D$ is a normal measure on $\kappa$ and $\{ \aleph_\alpha \colon > 2^{\aleph_\alpha} \le > \aleph_{\alpha+\beta}\} \in D$ (for some constant $\beta < \kappa$), then $2^\kappa > \le \aleph_{\kappa + \beta}$

He gives the following hint: If $f$ is such that $f(\aleph_\alpha) = \aleph_{\alpha+\beta}$ for all $\alpha < \kappa$, then $[f]_D = (\aleph _{ \kappa+j(\beta)})^M$

I think that I am just confused about the whole representation in $M$ and how to use it to solve this problem. Hints, partial or complete solutions are most welcomed.