   Chapter 11.4, Problem 41E

Chapter
Section
Textbook Problem

(a) Suppose that ∑ a n and ∑ b n are series with positive terms and ∑ b n divergent. Prove that if lim n → ∞ a n b n = ∞ then ∑ a n is also divergent.(b) Use part (a) to show that the series diverges.(i) ∑ n − 2 ∞ 1 ln n (ii) ∑ n − 1 ∞ ln n n

To determine

(a)

To prove:

If limnanbn= and bn is divergent then an is also divergent.

Explanation

1) Concept:

an and bn are series with positive terms then if

i) bn is convergent and anbn then an also converges.

ii) bn is divergent and anbn then an is also divergent.

2) Given:

limnanbn= and bn is divergent

3) Calculation:<

To determine

(b)

To prove:

i)

n=21lnn

ii) n=1lnnn bothare divergent by using  part (a)

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