Issues with gmail not recognising Google Play services
I believe it might not be a false alert... Your tablet may not be certified for Google Play, and that's probably why you are seeing this message.

Try this:


  On your computer browser, go to the Google Play Services app page on the Play Store: https://play.google.com/store/apps/d...roid.gms&amp;hl=en. Click the Installed button, and see if you can select your RCA tablet to install to.


Got it from here