They usually mean the same thing.
In some contexts /succession/ has the added meaning that subsequent terms
have a relation of 'parent to child', like: the succession of queens and kings of England.
This relation may be occasionally broken, still succession would be valid.
Another meaning of /succession/ is from this example:
when the President is unable to serve, the first in the line of succession would be
Are you talking about Mathematics ?
In this case /sequence/ is like /succession/ and /series/ implies a sum operation. Please give examples if this is the case.