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Real Analysis
book

Real Analysis

by V. Karunakaran
May 2024
Intermediate to advanced content levelIntermediate to advanced
585 pages
15h 38m
English
Pearson India
Content preview from Real Analysis
“real: chapter_10” 2011/5/22 23:26 page6—#6
10-6 Real Analysis
in some other cases, it will not converge at any point x with |x a|=R.
There are also cases wherein for some points x with |x a|=R the
series converges and for some other points x with |x a|=R the series
actually diverges. The following examples illustrate this fact.
Examples 10.2.5
1.
n=0
x
n
has radius of convergence 1 and does not converge for
points x with |x|=1.
2. As observed, already
n=1
x
n
n
2
has radius of convergence 1 but
converges for all points x with |x|=1.
3.
n=1
x
n
n
has radius of convergence 1 but converges at x =−1 and
does not converge at x = 1.
Remark 10.2.6 Let S denote ...
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Publisher Resources

ISBN: 9781299447561Publisher Website