Question

state and prove De’Alembart test or Ratio test.​

Answer 1

Answer:

Statement of D'Alembert Ratio Test

A series ∑un of positive terms is convergent if from and after some fixed term un+1un<r<1 , where r is a fixed number. The series is divergent if un+1un>1 from and after some fixed term. D'Alembert's Test is also known as the ratio test of convergence of a series.

Answer 2

Answer:

Statement of D'Alembert Ratio Test

A series ∑un of positive terms is convergent if from and after some fixed term un+1un<r<1 , where r is a fixed number. The series is divergent if un+1un>1 from and after some fixed term. D'Alembert's Test is also known as the ratio test of convergence of a series.

In mathematics, the ratio test is a test for the convergence of a series where each term is a real or complex number and aₙ is nonzero when n is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test