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

Yes

The word "servem" is identical in spelling, grammar, and meaning in both Brazilian and Continental Portuguese. It is the third-person plural present indicative of the verb servir (to serve). The only difference lies in pronunciation:

• In Brazilian Portuguese, the nasal diphthong "-em" is typically pronounced with a slight "i" sound at the end, sounding like /'seʁ.vẽj/ (resembling "ser-vẽ-ee").
• In Continental Portuguese, the "-em" is much more reduced and closed, often sounding like a simple nasalized vowel /'sɛɾ.vɐ̃/, with almost no audible "i" sound at the end.

Brazilian Portuguese Examples

1. Eles servem um café delicioso aqui no bairro. (They serve a delicious coffee here in the neighborhood.)
2. Esses tênis não servem mais nele. (Those sneakers don't fit him anymore.)
3. Os garçons servem a comida muito rapidamente. (The waiters serve the food very quickly.)
4. Essas chaves servem para abrir o portão da garagem. (These keys serve to open the garage gate.)
5. Os novos aplicativos servem para facilitar a vida dos usuários. (The new apps serve to make users' lives easier.)

Continental Portuguese Examples

1. Eles servem um café excelente nesta esplanada. (They serve an excellent coffee at this outdoor terrace.)
2. Estas chaves servem para a porta do autocarro. (These keys serve/work for the bus door.)
3. Os empregados servem o almoço com muita cortesia. (The employees serve lunch with much courtesy.)
4. Estas ferramentas servem para o trabalho no jardim. (These tools serve/are used for the garden work.)
5. Os copos servem para beber sumo de laranja. (The glasses serve to drink orange juice.)