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constructing unbounded sequence form non-decreasing, unbounded sequence

Source: Azerbaijan EGMO TST 2021, D2 P2

August 11, 2023
SequenceunboundedalgebraAZE EGMO TST

Problem Statement

Given a non-decreasing unbounded sequence an,a_n, construct a new sequence bnb_n as follows bn=a2−a1a2+a3−a2a3+...+an−an−1anb_n = \frac{a_2 - a_1}{a_2} + \frac{a_3 - a_2}{a_3} + ... + \frac{a_n - a_{n-1}}{a_n} Prove that bnb_n is also unbounded.
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