Is the word série the same in Brazilian and European Portuguese?

Yes

The spelling, meaning, and grammatical function of the word "série" are identical in both Brazilian and Continental Portuguese. The only difference is the pronunciation of the final unstressed "e":

• Brazilian Portuguese: The final "e" is pronounced clearly, typically as a long [i] sound (like the "ee" in "see").
• Continental Portuguese: The final "e" is an unstressed vowel that is heavily reduced, often sounding like a very short, neutral [ɐ] (similar to the "a" in "about") or even appearing to disappear in fast speech.

Brazilian Portuguese Examples

1. Eu adoro assistir a essa série. (I love watching this series.)
2. Ele está vendo uma série nova. (He is watching a new series.)
3. Houve uma série de imprevistos. (There was a series of unforeseen events.)
4. Essa série de livros é muito boa. (This book series is very good.)
5. Fizemos uma série de testes no carro. (We performed a series of tests on the car.)

Continental Portuguese Examples

1. Eu adoro ver esta série. (I love watching this series.)
2. Ele está a ver uma série nova. (He is watching a new series.)
3. Houve uma série de imprevistos. (There was a series of unforeseen events.)
4. Essa série de livros é muito boa. (This book series is very good.)
5. Fizemos uma série de testes ao carro. (We performed a series of tests on the car.)