The Entrepreneur writes in "5 Ways to Stop Embarrassing Yourself on LinkedIn":

LinkedIn is not Facebook, Instagram or any typical social network. It's a place to show your professional side, and that starts with your photo. A picture of you slamming beers won’t do; neither will a family reunion. You want a clean, professional headshot with a white or neutral background. If you don’t already have one, hire a professional photographer

And of course I could not agree more - you need a professional headshot to represent yourself in the right way on LInkedIn

Today it's the norm that we research each other way before we even meet - we look at LinkedIn profiles to determine if it's worth contacting you and to get an idea of your skills and competences

Hey, we even look at LinkedIn's suggestions for people we might know - and here there's a big chance that your picture will show up as a contact in the network of your network; what headshot would you like to represent you?

Having a professional headshot that shows you as just that, a business professional, is key. Should be obvious, but take a stroll through the people that LinkedIn suggests you as contacts and be amazed of the variety of headshots people wish to use as a professional representation of themselves

That should convince you ;-)

Also worth a read: "I can do my headshot myself"