d) i = 1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 46E
Related questions
Question
Part D
![Let V, = {xER|- :
for each positive integer i. Find each of the following. (Enter your answers using interval notation.)
(a)
4
Úv, - [-1,1]
i = 1
(b)
4
nVi =
i = 1
4' 4
(c) Are V,, V2, V31
mutually disjoint? Why or why not?
O Yes, because the union of the sets V,, V2, V3, ... is empty.
O Yes, because no two of the sets V,, Va, Va, ... have any elements in common.
V31
O Yes, because the intersection of the sets V,
1'
V2, V3'
V2, V31
... is empty.
O No, because no two of the sets V
1'
... are disjoint.
O No, because the sets V,, V, V2, ... are disjoint.
(d)
i = 1
(е) п
i = 1
(f)
ÜV, -
i = 1
(g) 00
i = 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd16c46a0-d8b3-4c49-8249-7270f2b9ceb6%2F656d9a0c-37b5-47dd-a758-1fdd05447757%2Fxtswrdw_processed.png&w=3840&q=75)
Transcribed Image Text:Let V, = {xER|- :
for each positive integer i. Find each of the following. (Enter your answers using interval notation.)
(a)
4
Úv, - [-1,1]
i = 1
(b)
4
nVi =
i = 1
4' 4
(c) Are V,, V2, V31
mutually disjoint? Why or why not?
O Yes, because the union of the sets V,, V2, V3, ... is empty.
O Yes, because no two of the sets V,, Va, Va, ... have any elements in common.
V31
O Yes, because the intersection of the sets V,
1'
V2, V3'
V2, V31
... is empty.
O No, because no two of the sets V
1'
... are disjoint.
O No, because the sets V,, V, V2, ... are disjoint.
(d)
i = 1
(е) п
i = 1
(f)
ÜV, -
i = 1
(g) 00
i = 1
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