a) Find A and B such that(12)*(4*+1_3k+1)(4* _3*)3* A+4k+1_3k+13kB4k _3kb) Use the result in part a) to find a closed form of the nth partial sum of the series(12)*Lik=1 (4k+1_3k+1)(4*–3*)and then find the sum of the series.3* B3k+1olacak seKgerlerini bulunuz.b) atentar emuz:!!eSerinin3n+1O A= 1, B = -3, Sn = 3 –Sum = 34"+1_3n+1,37O A= 3, B = -1, Sn = 4 –Sum44"-3" )3"+1O A= 1, B = -3, S, = 4Sum = 44"+1_3#+1 )37+1ОА- 3, В - —1,S, — 3 —,Sum = 34"+1_3n+1ОА-3, В — —1,S, — 3 —3"Sum = 34"-3" >

The solution to the given question is given below

a) Find A and B such that (12)* (4k+1_3k+1)(4* _3k) 3* A + 4k _3k 3*B 4k+1_3k+1 b) Use the result in part a) to find a closed form of the nth partial sum of the series (12)* Ek=1 (gki1_gk+1)(4* –3*) and then find the sum of the series.

a) Find A and B such that (12)* (4k+1_3k+1)(4* _3k) 3* A + 4k _3k 3B 4k+1_3k+1 b) Use the result in part a) to find a closed form of the nth partial sum of the series (12) Ek=1 (gki1_gk+1)(4* –3*) and then find the sum of the series.

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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Question

a) Find A and B such that
(12)*
(4*+1_3k+1)(4* _3*)
3* A
+
4k+1_3k+1
3kB
4k _3k
b) Use the result in part a) to find a closed form of the nth partial sum of the series
(12)*
Lik=1 (4k+1_3k+1)(4*–3*)
and then find the sum of the series.
3* B
3k+1
olacak seK
gerlerini bulunuz.
b) a
tentar emuz:
!!
eSerinin
3n+1
O A= 1, B = -3, Sn = 3 –
Sum = 3
4"+1_3n+1
,
37
O A= 3, B = -1, Sn = 4 –
Sum
4
4"-3" )
3"+1
O A= 1, B = -3, S, = 4
Sum = 4
4"+1_3#+1 )
37+1
ОА- 3, В - —1,S, — 3 —
,Sum = 3
4"+1_3n+1
ОА-3, В — —1,S, — 3 —
3"
Sum = 3
4"-3" >

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