3.7.3 For what series is the computation ak = k= 1 M azk + a2k-1 Thomson"Bruckner"Bruckner Elementary R 180 ClassicalRealAnalysis.com valid? Is this a rearrangement? 3.7.4 For what series is the computation Eax = _ (azk + 02k-1) k= 1 k=1 valid? Is this a rearrangement? 3.7.5 For what series is the computation ak = az tan tan tas + as tas t... k=1 valid? Is this a rearrangement?3.6.4 Let ax be a sequence of positive numbers and suppose that lim kak = L. K -+0o What can you say about the convergence of the series _jak if L = 0? What can you say if L > 0?3.6.10 * Show that the limit comparison test applied to series with positive terms can be replaced by the following version. If lim sup bk ak 0 CK and if _ _]CK diverges, then so does Zk=1 ak.3.5.13 Establish the Cauchy-Schwarz inequality: For any finite sequences {a1, a2, ..., an} and {b1, b2, ..., bn} the inequality n n N/ H [(ak ) ? n [ ( bk ) ? N/H k=1 k=1 k=1 must hold