r(r -- 1){r .3 3! where r is an arbitrary integral or fractional exponent. The necessary condition |x| < 1 for convergence was not stated by Newton. 8. Use the binomial theorem to obtain the following series expansions. – x³ + · . . (1+x)-1 = 1 – x +x? (a) + (-1)"x" + ·... (1– x)-2 = 1+ 2x + 3x² + . (b) %3D + (n + 1)x" +. ..

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Topic Video
Question

Number 8b

r(r -- 1){r
.3
3!
where r is an arbitrary integral or fractional exponent.
The necessary condition |x| < 1 for convergence was
not stated by Newton.
8. Use the binomial theorem to obtain the following
series expansions.
– x³ + · . .
(1+x)-1 = 1 – x +x?
(a)
+ (-1)"x" + ·...
(1– x)-2 = 1+ 2x + 3x² + .
(b)
%3D
+ (n + 1)x" +. ..
Transcribed Image Text:r(r -- 1){r .3 3! where r is an arbitrary integral or fractional exponent. The necessary condition |x| < 1 for convergence was not stated by Newton. 8. Use the binomial theorem to obtain the following series expansions. – x³ + · . . (1+x)-1 = 1 – x +x? (a) + (-1)"x" + ·... (1– x)-2 = 1+ 2x + 3x² + . (b) %3D + (n + 1)x" +. ..
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