2 3 () is equal to 1+ (x – 1) 1) Show that the sum of the series 1+ 2 +.. +... (x – 1)2 + (x –- 1)³ + ..+ (x – 1)" + as n → o and for |x| < 1.

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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2
3
1) Show that the sum of the series
1+
2
2
is equal to 1+ (x – 1)
+
+..+
•..
(x – 1)2 + (x – 1)³ + …+ (x – 1)" + .….as n → ∞ and for |x| < 1.
Transcribed Image Text:2 3 1) Show that the sum of the series 1+ 2 2 is equal to 1+ (x – 1) + +..+ •.. (x – 1)2 + (x – 1)³ + …+ (x – 1)" + .….as n → ∞ and for |x| < 1.
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