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- Using only the Archimedean Property of R give a direct E-N verification of the convergence of the following sequence: { [ 2 / (n^(1/2) ) ] + [ 1/n ] + 3 }Use the Cauchy Condensation test to prove that ∑ n = 2 to ∞ 1/( n (ln(n))^ p)) converges if p > 1 and diverges if p ≤ 1. (Make sure you verify that the hypothesis of the Cauchy Condensation test are met)Let (rn) be a sequence of real numbers. Show that the convergence of (sn) implies theconvergence of (|sn|).