my question is basically the title .
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It's tremendously exhausting to invite people to interact with you, everyone becomes tired of it after time. A good rule of thumb would be: "For every time he invites you - invite him; if he hasn't offered recently, send one invitation out there- after he responds, continue"
It's a tricky rule-of-thumb, but it works great. What I have noticed is that people are often scared of their first impression. Here's some psychology for those of you that are studying.
Your first impression lasts much longer compared to any influences you receive from that person. Therefor, the person you see as outgoing and funny, could have a horrible day - and you will still think they are outgoing and funny the next day.
SO -- to answer your question in a short way (haha). I would enjoy any woman that can invite me at least once a week to do something, it doesn't have to be all the time - but I would appreciate some effort; otherwise it seems like I would be doing a majority of the work to hang out.