For all a > 0 and b> 1, the inequalities In (n) ≤n, n < b are true for n sufficiently large (this can be proved using L'Hôpital's Rule). Let N be this sufficiently large n. Write an inequality comparing (In (n)) and n for n 2 N. (Express numbers in exact form. Use symbolic notation and fractions where needed.) inequality: 11 Incorrect Draw a conclusion about the convergence of Σ K Because 00 It is not possible to use the Direct Comparison Test to determine the convergence or divergence of n=1 (n(n))8 1- =1 n converges, 00 Σ #=1 (In (n))* (In (n)) also converges by the Direct Comparison Test. Because is a harmonic series, it diverges. Therefore, 11 =) 00 (In (n))* (In (n)) diverges by the Direct Comparison Test.
For all a > 0 and b> 1, the inequalities In (n) ≤n, n < b are true for n sufficiently large (this can be proved using L'Hôpital's Rule). Let N be this sufficiently large n. Write an inequality comparing (In (n)) and n for n 2 N. (Express numbers in exact form. Use symbolic notation and fractions where needed.) inequality: 11 Incorrect Draw a conclusion about the convergence of Σ K Because 00 It is not possible to use the Direct Comparison Test to determine the convergence or divergence of n=1 (n(n))8 1- =1 n converges, 00 Σ #=1 (In (n))* (In (n)) also converges by the Direct Comparison Test. Because is a harmonic series, it diverges. Therefore, 11 =) 00 (In (n))* (In (n)) diverges by the Direct Comparison Test.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:For all a > 0 and b> 1, the inequalities In (n) ≤n", n < b are true for n sufficiently large (this can be proved using
L'Hôpital's Rule).
Let N be this sufficiently large n. Write an inequality comparing (In (n)) and n for n > N.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
inequality: 11
Incorrect
Draw a conclusion about the convergence of
Σ
Because
00
It is not possible to use the Direct Comparison Test to determine the convergence or divergence of
n=1
(n(n))8
1- =1
n
converges,
00
Σ
#=1
(In (n))*
(In (n))
also converges by the Direct Comparison Test.
Because is a harmonic series, it diverges. Therefore,
11
00
(In (n))
(In (n))
diverges by the Direct Comparison Test.
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