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Infinite sums, convergence, accuracy.

What is the meaning of an infinite sum? This question has fascinated mathematicians for a long time; from Zeno's para-dox and the series of Madhava and Leibnitz to more contem-porary times. Euler, Fourier and others played insouciantly with infinite series until Abel, Cauchy and Weierstrass gave us a safe and dependable way to ``do the right thing" with in-finite series. Like other such instances in Mathematics, this did not shut the door on the older playground. Rather it pro-vided a framework to play in it with greater clarity.The author learned a lot about this the topic through the bookon $Divergent Series$ by G. H. Hardy, while teaching a course on ``Computational Methods" at IISER Mohali.

Kapil Hari Paranjape¹

1. ndian Institute of Science Education and Research Mohali Sector 81, SAS Nagar Manauli PO Punjab 140 306, India.

Published

10 July 2020