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Determine the limit superior and limit inferior of the following sequences how to find the M1,M2,M3,M4,M5,.....  CAN YOU EXPLAIN IT? I ALREADY CIRCLE IT

Determine the limit superior and limit inferior of the following sequences how to find the M1,M2,M3,M4,M5,.....  CAN YOU EXPLAIN IT? I ALREADY CIRCLE IT

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine the limit superior and limit inferior of the following sequences

how to find the M1,M2,M3,M4,M5,.....

 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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