5. A sequence of numbers u1,u2,U3,U4, . is defined by ... Un+1 : 4un + 2, where u = 2 Prove by induction that, for n E Z+, un ==(4" – 1) 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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x & こ
44
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5. A sequence of numbers u1,u2,U3,U4, ·
.. is defined by
Un+1
4un + 2,
where u = 2
2.
Prove by induction that, for n E Z+, un =÷(4" – 1)
3
z2r-1 if sin0 # 0
6. a) By considering z = cose + isin0, simplify E=1
(Hint. De' Moivres theorem will be useful)
b) Solve the inequality |x+ 3a| > 2|x – 2a\, a is a positive c
Transcribed Image Text:x & こ 44 (? 5. A sequence of numbers u1,u2,U3,U4, · .. is defined by Un+1 4un + 2, where u = 2 2. Prove by induction that, for n E Z+, un =÷(4" – 1) 3 z2r-1 if sin0 # 0 6. a) By considering z = cose + isin0, simplify E=1 (Hint. De' Moivres theorem will be useful) b) Solve the inequality |x+ 3a| > 2|x – 2a\, a is a positive c
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