… access on my Samsung tablet using chrome Web browser but can neither sign in nor watch.
Did you go to tv.apple.com? Did you find the blue ‘Sign In’ button in the upper right corner?
What happens instead, when the sign-in doesn’t work? Do you get an error message? What does it say?
Have you tried other browsers? Apple suggests Firefox as option too.
Depending on the age of the tablet, the browser makers might present a legacy version, which may not play well with the most modern web technologies. What version browser do you have on the tablet?
Don’t go changing browser settings too much. Apple TV+ should work with default settings, but there are settings that can prevent it from working correctly.
If your browser uses ad blockers/content blockers/element blockers, then exclude apple.com for that.
All the ways to watch Apple TV+ and more - Apple Support
… wish to watch a series only available on this service …
Some are very, very good. I hope you get it working.