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Double Series 1

We define the notion of a double sequence, iterated limits and convergence of a double sequence. We give a few examples to illustrate the concepts and their differences. We then define a double series, its convergence and the iterated sums. Timestamp compiled from the inputs of Ishwarya and Priyanka Vaidheesh. 0:00 Introduction 0:43 Brief explanation about this lecture series 1:26 Defining Double sequences 6:25 Motivation to find limit of the double sequence 11:08 Convergence of Double Sequence 12:36 Counter example which shows that Iterated limit may exists but the sequence not convergent 18:05 Example for Sequence is convergent but the Iterated limits do not exist 23:20 Main result on the equality of all the three limits. 30:11 Diagonal sequence in double sequence also converges to the same limit 31:39 When is a double sequence Cauchy? 35:00 If double sequence is Cauchy then it is convergent. 41:08 Quick Summary