- #1

beebeeamoras

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Prove that the following statement are equivalent;

(i) f(x)--->a, as x--->oo

(ii) for every sequence {x_n} of positive numbers such that x_n --->oo one has that

(1/n)\sum f(x_k)--->a, as n--->oo (the sum is taken from k=1 to k=n)