Uh, according to Wikipedia the word comes from Greek (like so many other in English), 'synergia συνεργία from synergos, συνεργός, meaning "working together"'. They do mention that Buckminster Fuller analysed it further, and coined "synergetics". See http://en.wikipedia.org/wiki/Synergy.

Oh, and to the grandparent (I think), it was fun to see "M&A" used in a thread about opaque language. Turns out it stands for "mergers and acquisitions" (http://en.wikipedia.org/wiki/M%26A).