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ISI 2020 : Problem 4

Source: B.Stat & B.Math Entrance Exam 2020

September 20, 2020
isi2020real analysis

Problem Statement

Let a real-valued sequence {xn}n⩾1\{x_n\}_{n\geqslant 1} be such that lim⁡n→∞nxn=0\lim_{n\to\infty}nx_n=0 Find all possible real values of tt such that lim⁡n→∞xn(log⁡n)t=0\lim_{n\to\infty}x_n\big(\log n\big)^t=0 .
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