Consider a group of \(N=100\) relativistic houseflies, flying along the x-axis. Each fly \(F_{k}\) sees the next fly \(F_{k+1}\) moving away at \(u=0.01 c\) (c is the speed of light). What is the relative speed \(v_{100}\) **in meters per second** between the leftmost fly, \(F_{1}\), and the last fly, \(F_{100}\)?

**Details and assumptions**

Assume \(c=3\times 10^{8}~\text{m}/\text{s}.\)

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