Totally agree with what Adam said, you need all your stats all your proof with good conversions. Even then many will not take you seriously.

One way I have used in the past is to see if any of my current contacts knows the person I wish to connect with. They then introduce me to them and that way they take you a lot more serious.

A recommendation goes a long way rather than approaching cold. That being said it is also a good habit to introduce your contacts to others to all collectively grow and expand together.

If approaching cold try sending them $10 in paypal, sending them a letter, sending them a gift using Fedex with a letter inside, voucher etc. Get creative - something that stands out.

Hope this helps!