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Romanian District Olympiad 2019 - Grade 11 - Problem 1

Source: Romanian District Olympiad 2019 - Grade 11 - Problem 1

March 16, 2019
limitSequencesConvergencecalculus

Problem Statement

Let (an)n≥1(a_n)_{n \ge 1} be a sequence of positive real numbers such that the sequence (an+1−an)n≥1(a_{n+1}-a_n)_{n \ge 1} is convergent to a non-zero real number. Evaluate the limit lim⁡n→∞(an+1an)n. \lim_{n \to \infty} \left( \frac{a_{n+1}}{a_n} \right)^n.
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