persevere

Using the word persevere: 'This woman has persevered in her carreer'. Is the word used correctly?

It is fine.

My grandmother used to infuriate me as a small child when I was cleaning her carpets and finding it heavy work by saying "Persevere, persevere, persevere". Grandmothers can be very tactless.

Thanks. Umm... Did you clean the carpets or did you beat them perseverely?:-)