S
2
True/False
1 —u
an alternating series of the form a
±a:—ai+... ifu >
2
aiid lini a = 0. then the series converges.
> 0
1. For
T
2. A series that. converges cOn(litionally also converges absolutely.
[o1\’JP(LS
‘j
l,s&
3. A series converges absolutely in the interior of it.s convergence set.
4. You can find a Taylor series about. any point. x=a for any function f(x).
f{
n
5. For an alternating series if the absolute ratio test give B=0, then the
series converges conditionally.
1
io\t
3
oLl
Ctej
3
b1
1
R<
1’
1
(jJ
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)
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C
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5
5
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3
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8
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k
7:3
:5
9j;,
—
,
p
)
)
çF
p
F
0
(A
(I’
Determine whet her I he following series (Ofl(Iit jonally converges. al)SOIUt ely
converges, or diverges.
cos(n-ir)
—
4
—
5
n
St
e
(1’
(— I’)
n
I
n
P-
clm ‘J
fl-;j
Co5 (nil’)
n
Ct, 1vJfyS
Cc5
b
n
V’
6
-
V
)Jj
0
0
S
3
-
II
jRs)JI
7i
p
I’
1
I
I
1
3
fr
I
IJ
M8
-‘
I
+
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S
C
C
‘I
C’,
C
,__•
C’.
I’
—.
(0
I
0
‘C
+
fl
n
C.
C
j
-
-4-
0
O
a
8tIN&
C
a
p
c
C’
-
_\c
CC
oc
=
C
C
—
C
.-
-c
C
—
C
-4-
—
—
C
C
—
—
2.
-c
—
—
1
_\C.
/
ci
-
‘I
8vc
L)
7. (Jsing the Maclaurm series you found in 1)robleln 5 solve for the power
of
g(x)
Ii,
=
1+x
ç71
C-,.
nI
(i-x)
(-‘)
)(
n
vWl
=
fl
I
(Yr\
Cc
(-“)
(-i
fc
10
\::
S)
9.)
¶1
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