- (a) Starting with the geometric series ox", find the sum n=0 of the series Σnxt Σηx |x| < 1 пх n=1 (b) Find the sum of each of the following series. п ( ) Σηx", | x1<1 (ii) E 2" n=1 (c) Find the sum of each of the following series. (i) E n(n – 1)x", |x|< 1 n=2 2² – n (ii) 2 2" (iii) E 2" n=2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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- (a) Starting with the geometric series ox", find the sum
n=0
of the series
Σnxt
Σηx
|x| < 1
пх
n=1
(b) Find the sum of each of the following series.
п
( ) Σηx", | x1<1
(ii) E
2"
n=1
(c) Find the sum of each of the following series.
(i) E n(n – 1)x", |x|< 1
n=2
2² – n
(ii) 2
2"
(iii) E
2"
n=2
Transcribed Image Text:- (a) Starting with the geometric series ox", find the sum n=0 of the series Σnxt Σηx |x| < 1 пх n=1 (b) Find the sum of each of the following series. п ( ) Σηx", | x1<1 (ii) E 2" n=1 (c) Find the sum of each of the following series. (i) E n(n – 1)x", |x|< 1 n=2 2² – n (ii) 2 2" (iii) E 2" n=2
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