i) Let {n} a sequence of non-negative terms that is monotone decreasing and în → 0. If SnX1 X2 + x3 = ... • (-1)n-¹ xn prove that the sequence {sn} converges using the Cauchy criterion. [Hint: You need to prove that {sn} if m > n Sm Sn = (-1)"xn+1 - ... + (−1) m−¹ xm = (−1)″ (xn+1 + ... + (−1)m-n−¹xn), then use the associative property of the sum and the fact that {n} is monotone decreasing and în → 0.]

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