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Determine by true or false the following questions. If true, briefly explain it. If false, provide a counterexample. (i) [2 points] Let {an}₁ be a positive sequence such that Σ1 ªn < ∞, then =1 +an+2125|) = 0. lim (an+ N→∞ (ii) [2 points] Let f, g : [0,2] → R be two functions such that f is continuous but g is discontinuous, then the sum function f + g is always discontinuous. (iii) [2 points] Every differentiable function f : [0, 1] → R is integrable on [0, 1].