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:

Explain how they provide a counterexample to the Limit Comparison Test when the series are not assumed to be positive.

Transcribed Image Text:

Σ n=1 (-1)" √n n=1 (-1)" √n 1 + (-1)" √n