I would like to know this as well.

Wouldn't recommend that to you even if that was possible because linkedin is an awesome platform that has B2B people congregating on it, more personalized message you can craft for each individual, better response you will get

Agree with James. Don't mass message on LinkedIn. You will lose many connections. Even if you are offering a service, talk to your connections one on one. Introduce yourself, make it personal, and you have a chance. A mass message is going to be considered spam.

Linked messaging with linked messages will not go down well unless you know the contacts very well.

Spamming in anything generally isn't a good idea. Personalize your messages to who you want to create a relationship with and you're going to see a lot better results.

Oh - so you can spam people that don't want to hear from you?

Yeah - great idea!