MathDB
JBMO Shortlist 2023 A7

Source: JBMO Shortlist 2023, A7

June 28, 2024
SequenceinequalitiesJBMOJBMO Shortlistalgebra

Problem Statement

Let a1,a2,a3,…,a250a_1,a_2,a_3,\ldots,a_{250} be real numbers such that a1=2a_1=2 and
an+1=an+1an2a_{n+1}=a_n+\frac{1}{a_n^2}
for every n=1,2,…,249n=1,2, \ldots, 249. Let xx be the greatest integer which is less than
1a1+1a2+…+1a250\frac{1}{a_1}+\frac{1}{a_2}+\ldots+\frac{1}{a_{250}}
How many digits does xx have?
Proposed by Miroslav Marinov, Bulgaria
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