The MeansAs is customary, group a finite sequence of numbers a1, a2, ..., an in a vector form a = (a1, a2, ..., an). The arithmetic and harmonic means of the sequence defined as
where the summation is being carried from i = 1 through i = n. Observe that H(a) = 1/A(1/a). This leads to a more general definition
where I assume that all ai's are positive and r is a real number different from 0. For example, A(a) = M1(a) whereas H(a) = M-1(a). In general, Mr(a) is the mean value of numbers a1, a2, ..., an with the exponent r. M2(a) is known as the quadratic average. For r = 0, the following complements the definition of Mr(a):
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