Did you know that administrators of LinkedIn Groups can send group announcements to all members of their group who’ve not opted out of those announcements (they’re turned on by default so most members receive them).
These announcements can be sent up to once per week and are completely free as part of your participation in LinkedIn as a group administrator. You can’t send them in any format other than plain text though there does not appear to be any restriction on what you can insert to the mailing – including links to your own web site outside of the LinkedIn group.
Access the feature from the group’s manage menu. And for even more reach consider opening up your LinkedIn Group to the public so that links you may share can be browsed even by non-group members.