Since anyone can open a Gmail address & end spammy email, it seems pretty obvious using any public email service as a newsletter sender address is not a good idea.
So the short answer is: you can’t do that with a Gmail address (or Yahoo, Hotmail, …).
A real pro solution is to get yourself a dedicated domain name for that.
Using Mailjet & Mailchimp, you have to create new entries in your DNS console. Mailchimp explains this here: http://kb.mailchimp.com/delivery/deliverability-research/set-up-custom-dkim