21(a). Show how the general formula Mr encompasses various types of common averages and including (as limit) the geometric average (have a look at the proof)
If p is a non-zero real number, and x1 , … , xn are positive real numbers, then the generalized mean or power mean with exponent p of these positive real numbers is:
For p = 0 we set it equal to the geometric mean (which is the limit of means with exponents approaching zero, as proved below):
Special cases:-
