(iii) Consider b= In an], where In denote the natural logarithm of real numbers. Using Monotone Convergence Theorem, explain whether the sequence {b} is convergent. (iv) Find lim b, in (iii) if exists. (v) Examine whether {b} in (iii) is a Cauchy sequence using definition (e-6).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the set
Sn = {ann € N},
¹(+1).
(iv) Find lim b, in (iii) if exists.
=(-1)+1
(iii) Consider b₁ = In an], where In denote the natural logarithm of real numbers.
Using Monotone Convergence Theorem, explain whether the sequence {b} is
convergent.
(v) Examine whether {b} in (iii) is a Cauchy sequence using definition (e-6).
(vi) Can Bolzano-Weierstrass Theorem be applied to the sequence {b} in (iii)? In
any case (yes or no), justify the reason with a supporting example.
Transcribed Image Text:Consider the set Sn = {ann € N}, ¹(+1). (iv) Find lim b, in (iii) if exists. =(-1)+1 (iii) Consider b₁ = In an], where In denote the natural logarithm of real numbers. Using Monotone Convergence Theorem, explain whether the sequence {b} is convergent. (v) Examine whether {b} in (iii) is a Cauchy sequence using definition (e-6). (vi) Can Bolzano-Weierstrass Theorem be applied to the sequence {b} in (iii)? In any case (yes or no), justify the reason with a supporting example.
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