# Relativistic flies

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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