MathDB
Another integral sequence (last)

Source:

October 31, 2019
calculusintegrationreal analysissequence of integralsDefinite integral

Problem Statement

Let be the sequence (Jn)n≥1, \left( J_n \right)_{n\ge 1} , where Jn=∫(1+n)21+(1+n)2x−1−n−n2x−1dx. J_n=\int_{(1+n)^2}^{1+(1+n)^2} \sqrt{\frac{x-1-n-n^2}{x-1}} dx. a) Study its monotony. b) Calculate lim⁡n→∞Jnn. \lim_{n\to\infty } J_n\sqrt{n} .
Ion Bursuc
Back to ProblemsView on AoPS