Math Problem Statement

University of Ibadan, B.Sc. Degree Examination (2022/2023) - MAT 222: Analysis. The exam contains questions on topics like bounded subsets of real numbers, sequences, convergence, and series. Specific questions include proving the completeness of rational numbers, analyzing sequences and their properties, and evaluating series for convergence.

Solution

The document you've uploaded is a mathematics examination paper, specifically for a B.Sc. degree in Analysis. It includes questions on topics like bounded subsets of real numbers, sequences, convergence, and series.

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Math Problem Analysis

Mathematical Concepts

Bounded subsets of real numbers
Supremum and infimum
Rational and real numbers
Convergence of sequences
Bounded and monotone sequences
Series convergence

Formulas

lim (n→∞) (an)
Supremum and infimum properties
Formula for series convergence: Σ ak

Theorems

Bolzano-Weierstrass theorem
Monotone Convergence Theorem
Properties of supremum and infimum

Suitable Grade Level

Undergraduate (Mathematics, Second Year)