Iterated collinear boosts with equal rapidity
= Iterated collinear boosts with equal rapidity
{title2=$u_n=c\tanh(n\alpha)$}
The <relativistic velocity-addition formula> becomes addition of <rapidities> for collinear <Lorentz boosts>. Starting from rest, applying the same positive rest-frame <velocity> increment $c\tanh\alpha$ repeatedly gives $u_n=c\tanh(n\alpha)$. For increment $c/2$, $\alpha=\tfrac12\log3$ and $u_n=c(3^n-1)/(3^n+1)$. Every finite sequence remains below the <speed of light>.