Such expressions as
are plural or singular?
I like to watch drama/TV series or I like to watch a drama/TV series?
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"Series" can be singular or plural depending on context. Both of your sentences are therefore correct but different.
I like to watch TV series.
uses series as a plural and means you like to watch a number of different TV shows.
I like to watch a TV series.
uses series as singular and means you like to watch one TV show.
The word series is both singular and plural.
Good information from thefreedictionary quoting American Heritage Dictionary as its source:
Series is both a singular and a plural form. When it has the singular sense of "one set," it takes a singular verb, even when series is followed by of and a plural noun: A series of lectures is scheduled. When it has the plural sense of "two or more sets," it takes a plural verb: Two series of lectures are scheduled: one for experts and one for laypeople.
Our concern is series in broadcasting. So,
a set of radio or television programs that deal with the same subject or that have the same characters.* -OALD
Having this said, you watch a TV series. And yes, do consider Nigel's answer if you are specific about one particular program or series.