Chapter 1.15, Problem 28P

The energy of an electron at speed $\nu$ in special relativity theory is $m{c}^2{(1-{\nu }^2/c^2)}^{-1/2}$ where m is the electron mass, and c is the speed of light. The factor mc² is called the rest mas energy (energy when $\nu =0$). Find two terms of the series expansion 0f ${(1-{\nu }^2/c^2)}^{-1/2}$ and multiply by mc² to get the energy" at speed $\nu$.

What is the second term in the energy series? (If $\nu /c$ is very small, the rest of the series can be neglected; this is true for everyday speeds.)