44. Assumptions Matter In 1829, Lejeune Dirichlet pointed out that the great French mathematician Augustin Louis Cauchy made a mistake in a published paper by improperly assuming the Limit Comparison Test to be valid for nonpositive series. Here are Dirichlet's two series: n=1 (-1)" √n n=1 (-1)" √n 1+ (-1)") √√n Explain how they provide a counterexample to the Limit Comparison Test when the series are not assumed to be positive.

44. Assumptions Matter In 1829, Lejeune Dirichlet pointed out that the great French mathematician Augustin Louis Cauchy made a mistake in a published paper by improperly assuming the Limit Comparison Test to be valid for nonpositive series. Here are Dirichlet's two series: n=1 (-1)" √n n=1 (-1)" √n 1+ (-1)") √√n Explain how they provide a counterexample to the Limit Comparison Test when the series are not assumed to be positive.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 82E

See similar textbooks