Originally posted by KazetNagorra
It's a Taylor series expansion around v = 0.
See also: http://www.wolframalpha.com/input/?i=m*c^2%2F%28sqrt%281-%28v%2Fc%29^2%29%29
ok, so the other terms have little signifigance if v is relatively small when compared to "c".
Given the first 2 terms
mc^2 + 1/2*m*v^2
I suppose I incorrectly thought there was physical significance to the remaining terms, as the series would lead me to believe, given the KE from classical mechanics, and the first term synonomous with Einstein and relativity.
I find it funny that we found the second term first, certainly the first term was well deserved to be found second leading to a new piece of the infinite jigsaw puzzle.