Assume that we have a function for an application of the form F(i, p), which gives the fraction of time that exactly i processors are usable given that a total of p processors is available. That means that

Assume that when i processors are in use, the applications run i times faster. Rewrite Amdahl€™s law so it gives the speedup as a function of p for some application.

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Σ F(i, p) = 1 i = 1