Let {an}o be a sequence with positive terms. (a) Prove that if lim van= ∞, then La, diverges. (b) Prove that if lim van= L> 1, then Can diverges. Hint. Start by using the definition of that limit to show that there is an r > 1 such that, for sufficiently large n, Van >r. (c) Prove that if lim yan= L< 1, then Ca, converges. %3D
Let {an}o be a sequence with positive terms. (a) Prove that if lim van= ∞, then La, diverges. (b) Prove that if lim van= L> 1, then Can diverges. Hint. Start by using the definition of that limit to show that there is an r > 1 such that, for sufficiently large n, Van >r. (c) Prove that if lim yan= L< 1, then Ca, converges. %3D
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 25RE: Use the formula for the sum of the first nterms of a geometric series to find S9 , for the series...
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