View answer: Assign a grade of A (correct), C (partially correct), or F (failure) to

Chapter 4, Problem 10

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Assign a grade of A (correct), C (partially correct), or F (failure) to each.Justify assignments of grades other than A.(a) Claim. If two sequences x and y both diverge, then diverges.Proof. Suppose Since x diverges, there exists1 > 0 such that for all there exists such that N n > Nlimn(xn + yn) = L.x + yxn = 1 if n = 12xn1 if n 2.xn = d if 3 n = 12xn1 if n 2.Since y diverges, there exists such that, for 2 > 0 | xn L2 | 1.all there exists such that LetThen for all there exists such thatTherefore, (b) Claim. If the sequence x converges and the sequence y diverges, thendiverges.Proof. Suppose for some real number K. Sincefor some number L, that is,yn K L. This is a contradiction. Thus diverges. xn