how to find the M1,M2,M3,M4,M5,.....m1,m2,m3,...  CAN YOU EXPLAIN IT? I ALREADY CIRCLE IT

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 2E
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how to find the M1,M2,M3,M4,M5,.....m1,m2,m3,...

 CAN YOU EXPLAIN IT? I ALREADY CIRCLE IT

E sin (.
3D1
The terms in the sequence are
{1.0,-3,0,금,0,-, 0, 금,0;-2. .
112
We have
1
M, = 1, M2 =
M3
52
1
M4 =
M5 =
52
52
1
1
1
1
M6 =
M, =
92
Mg =
92
, M, = -
92
92
Therefore
1
M1 = 1,
Mạn-2
(4n + 1)2'
Man-1 =
(4n + 1)2
1
Man =
Man+1
n = 1,2, 3, ..
%3D
(4n + 1)2'
(4n + 1)2
and we have
lim sup u, = lim M, = 0.
In a similar manner,
1
m1 =
• m2 = -
32
32
1
1
1
Me =-.
72
72. m, = -
72
=
72
m, =-
m,
1
1
1
Mg = -
112
mg
M10 =
M11 =
112
112
112
Therefore,
1
m1 = -
12. m2 =-.
E, m3 = -
1
man =
man+1 = -
(4n + 3)2'
(4n + 3)2
1
1
man+2
man+3
n = 1,2,3, ..
(4n + 3)2 '
(4n + 3)2
Thus,
lim inf un = lim m, = 0.
Transcribed Image Text:E sin (. 3D1 The terms in the sequence are {1.0,-3,0,금,0,-, 0, 금,0;-2. . 112 We have 1 M, = 1, M2 = M3 52 1 M4 = M5 = 52 52 1 1 1 1 M6 = M, = 92 Mg = 92 , M, = - 92 92 Therefore 1 M1 = 1, Mạn-2 (4n + 1)2' Man-1 = (4n + 1)2 1 Man = Man+1 n = 1,2, 3, .. %3D (4n + 1)2' (4n + 1)2 and we have lim sup u, = lim M, = 0. In a similar manner, 1 m1 = • m2 = - 32 32 1 1 1 Me =-. 72 72. m, = - 72 = 72 m, =- m, 1 1 1 Mg = - 112 mg M10 = M11 = 112 112 112 Therefore, 1 m1 = - 12. m2 =-. E, m3 = - 1 man = man+1 = - (4n + 3)2' (4n + 3)2 1 1 man+2 man+3 n = 1,2,3, .. (4n + 3)2 ' (4n + 3)2 Thus, lim inf un = lim m, = 0.
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