5. Let (an) be a Cauchy sequence. Suppose that for each H = N, there is an m(H) Є N with m(H) > H such that am > 0, and there is an k(H) Є N with k(H) > H such that ak < 0. Prove that lim(an) = 0, using only the definition of Cauchy sequence and the e K definition of limits. -

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