Google recently pushed the factory images of the Android 5.1 Lollipop and even released it to numerous devices including the Nexus 5. Now the tablets are going to get the Android 5.1 update starting off with the Nexus 10 tablet.
The Nexus 10 is getting a 104.4 MB file bearing OTA Android 5.1 update with LMY47D build. This version mostly brings performance tweaks, several bug fixes and under-the-hood changes to achieve stability.
This update will be rolled out in phases and that means it might take a day or more to reach your Nexus 10 tablet. Do note that the tablet should be at least 50 % charged to install the OTA update.