MathDB

Find the limit of this saequence

Source: 2019 Jozsef Wildt International Math Competition-W. 9

May 18, 2020

limitSequences

Problem Statement

Let

\alpha > 0

be a real number. Compute the limit of the sequence

\{x_n\}_{n\geq 1}

defined by

x_n=\begin{cases} \sum \limits_{k=1}^n \sinh \left(\frac{k}{n^2}\right),& \text{when}\ n>\frac{1}{\alpha}\\ 0,& \text{when}\ n\leq \frac{1}{\alpha}\end{cases}