I just noticed this. I never did before.
Only when you personalize a connection request (as was done in the second of these 3 open requests), can the recipient message you back. Not so if you send the boiler plate, dull drab. boring “I’d like to connect to you on LinkedIn,” as in the first and the third.
Give the recipient the opportunity to reply, to ask you a question back, or whatever response they deem necessary. Almost like a free INmail…
Ask professionally and give the recipient context where and how you met, why you can help him/her.
Don’t be lazy, for yet this as another reason, don’t send the standard connection request.
No one wants to connect to someone who is average, standard. We seek quality colleagues to surround ourselves. You should be perceived as quality as you add colleagues.