Which of the following statements are true? Vn² sin(n²) n +1 I. lim = 1. II. Let {an} be a convergent sequence of real If ba a1 + .. + an numbers. then the sequence {bn} is also convergent and lim bn lim an arctan n III. lim 0. 4n

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Calculus II

Which of the following statements are true?
Vn² sin(n²)
lim
I.
= 1.
n +1
II. Let {an} be a convergent sequence of real
a1 +. + an
numbers.
If bn
then
the sequence {bn} is also convergent and
lim bn
lim an-
arctan n
III.
lim
0.
4n
IV. Lemma: For any sequence {an} of real numbers,
lim a2k = lim a2k+1 = L if and only if
lim an = L; (L ER).
n+00
By the lemma above, one can obtain that
1
(-1)"-1n
= - - - + -
if an
4
- - +
n
1
then lim Jan|
(a)
I, III
(b)
III, IV
П, IV
(d)
I, II, III
(c)
(e)
II, III, IV
Transcribed Image Text:Which of the following statements are true? Vn² sin(n²) lim I. = 1. n +1 II. Let {an} be a convergent sequence of real a1 +. + an numbers. If bn then the sequence {bn} is also convergent and lim bn lim an- arctan n III. lim 0. 4n IV. Lemma: For any sequence {an} of real numbers, lim a2k = lim a2k+1 = L if and only if lim an = L; (L ER). n+00 By the lemma above, one can obtain that 1 (-1)"-1n = - - - + - if an 4 - - + n 1 then lim Jan| (a) I, III (b) III, IV П, IV (d) I, II, III (c) (e) II, III, IV
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