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mespilus-
1/6
Why 1/6, rather than 1/3 or 1/4?
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It's a taylor expansion of the gamma factor and the full relativistic energy/mass equivalence.
Second answer here explains better than I can: https://www.reddit.com/r/askscience/comments/2r0dtk/are_the_emc2_and_ek12mv2_equations_connected/
The later terms are negligible as they start to include division by increasing powers of c.
And physics stackexchange is fairly authoratative: https://physics.stackexchange.com/questions/435951/what-do-the-small-terms-in-the-series-expansion-of-relativistic-energy-mean
gbj_tester
Backstop
What's the first? Typically you need at least 3 terms in a sequence in order to deduce a rule which will allow construction of an arbitrary term or element in the sequence.