1905 paper "Does the Inertia of a Body Depend Upon its Energy-Content? In his 1905 paper Einstein uses a Taylor expansion and keeps only the first term (an approximation) to derive E=mc^2 which is good if v<<c but if v is not <<c then we need more terms. If we keep the first three terms then mc^2 is divided by (1 + 3/4(v/c)^2 + 15/8(v/c)^4) have I done the Taylor series correctly? Do we all agree? This number of terms would be good as long as (v/c)^4 <<1 say up to v=0.4c. Is this correct?