Equal-rapidity chain of collinear Lorentz boosts
= Equal-rapidity chain of collinear Lorentz boosts
{title2=$v_N=c\tanh(N\operatorname{artanh}(u/c))$}
If each successive <inertial frame> moves at the same signed <velocity> $u$, with $|u|<c$, relative to the preceding frame along a common axis, the <rapidity> adds. The final <velocity> relative to the first frame is therefore the displayed expression. When $u=c/N$ and $N\ge2$, the limit is $c\tanh1$, since $N\operatorname{artanh}(1/N)\to1$.