Answered: 11) Suppose an>0. Which of the… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 54E

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Question

pleasssssssse solve question 11

10) If 2 an = 12, then lim an =
848
n=1
(A) 1
8
(A) If lim
11) Suppose an > 0. Which of the following is (always) correct?
an 1
3
n-x 6n
(B) 2
(D)
-
(A) Σ
n=0
8WiWi
then
(B) If an> for all n, then an is convergent
(C) 0
n=0
n=1
(C) If an < for all n, then an is divergent
z3n+5
(2n)!
(D) If an is decreasing with f(n) = an and
(E) If an>()" for all n, then
(E)
an is convergent
n=1
8
12) The Maclaurin series for rx5 cos(x³)
(-1)"x6n+5
(2n)!
M8
n=1
n=0
∞
n=1
8
(Β) Σ
n=0
(D) 12
an is divergent
x6n+5
(2n)!
(-1)^²n+5
(2n)!
(E) 6
f(x)da = 4, then a = 4
n=2
8
(C) Σ
n=0
8
(-1)"p³n+5
(2n)!

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i. Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given by the even terms of sn and that given by the odd terms of sn both converge to 3.) Show that also limn→∞ sn = 3.ii. Give an example of a sequence where the sequences given by the even and by the odd terms both converge, but where the entire sequence does not converge.
i. Suppose that the sn satisfies both limn→∞s2n = 3 and limn→∞s2n+1 = 3. (That is, the sequence given by the even terms of sn and that given by the odd terms of sn both converge to 3.) Show that also limn→∞sn = 3.ii. Give an example of a sequence where the sequences given by the even and by the odd terms both converge, but where the entire sequence does not converge.
Suppose that {xn} is a sequence of real numbers satisfying lim (as n→∞) xn = 1. prove that lim (as n→∞) (1 + 2xn) = 3.
A sequence (xn)∞ {n=1} is said to oscillate if lim inf xn < lim sup xn. Prove or disprove the following. a) Every oscillating sequence diverges. b) Every divergent sequence oscillates. c) Every oscillating sequence has a convergent subsequence.
E. i. Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given by the even terms of sn and that given by the odd terms of sn both converge to 3.) Show that also limn→∞ sn = 3.ii. Give an example of a sequence where the sequences given by the even and by the odd terms both converge, but where the entire sequence does not converge. .

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